can someone help answer and explain to me how to solve this? log (lowercase 6) 1/36
Answers
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Explanation:
We will use the log rule that log(x^y) = y*log(x). Call this log rule 1. This log rule basically allows us to pull the exponent down.
Another log rule that we will use is [tex]\log_x\left(x\right) = 1[/tex] where x is any positive real number but x = 1 is NOT allowed. Call this log rule 2.
Because 36 = 6^2, this means that 1/36 = 6^(-2)
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So,
[tex]\log_6\left(\frac{1}{36}\right)=\log_6\left(\frac{1}{6^2}\right)[/tex]
[tex]\log_6\left(\frac{1}{36}\right)=\log_6\left(6^{-2}\right)[/tex]
[tex]\log_6\left(\frac{1}{36}\right)=-2*\log_6\left(6\right)[/tex] Use log rule 1 (see above)
[tex]\log_6\left(\frac{1}{36}\right)=-2*1[/tex] Use log rule 2 (see above)
[tex]\log_6\left(\frac{1}{36}\right)=-2[/tex]
This means that the given expression simplifies to -2
You can use a calculator to type in "log(1/36)/log(6)" without quotes and you should get -2 as the answer
so 6² = 36
therefore, 6⁻² = [tex] \frac{1}{36} [/tex]
so your answer will be -2
the power is the answer
Related Questions
Mayumi is constructing a line through point P that is perpendicular to RS←→. She places her compass on point P to construct an arc. What must be true about the width of the compass opening when Mayumi draws the arc?
A. It must be equal to PS .
B. It must be greater than 12RS.
C. It must be wide enough so that the arc intersects RS←→ in two points.
D. It must be equal to PR .
Answers
Answer:
Width of the compass should be more than the smallest space between P and RS, so that it cuts RS at two distinct points. Therefore, it must be wide enough so that the arc intersects RS←→ in two points. The photo is attached so that you can understand it more.
Maria gathered the data in the table. She finds the line of best fit to be y = 2.78x – 4.4. What is the residual value when x = 4?
Answers
You plug 4 into the line of best fit and get 6.72. This is your predicted value, but the residual is the difference between the actual value and predicted. So you subtract: 7.3-6.72=0.58.
Solution:
The line of best fit is given as y=2.78x-4.4
We need to find the residual value when x=4.
The residual value is an estimate of the wholesale value .To find the residual value we plug in x=4 in the given line of best fit.The corresponding y value will give the predicted value.
y=2.78x-4.4
Substituting x=4,
y=2.78(4)-4.4
y=11.12-4
y=7.12.
The predicted value when x=4 is y=7.12.
Residual value = predicted value - Actual value -=7.12 - actual value.
Of 60 students, 24 students have a pet. What is the ratio of students with pets to students without pets?
Answers
Hope this helps
the ratio of students with pets to without pets is 24:36
or simplified: 2:3
hope this helps
In a test-cross of a heterozygous black guinea pig (bb), what is the probability that the first two (2) offspring will be white?
Answers
In triangle ΔABC, ∠C is a right angle and CD is the height to AB, Find the angles in ΔCBD and ΔCAD if: m∠A = α
m∠DBC =
m∠DCB =
m∠CDB =
m∠ACD =
m∠ADC =
Answers
Given:
m∠C = 90°, because ∠C is a right angle.
m∠D = 90°, because CD is the height to AB.
m∠A = α
Because the sum of angles in a triangle is 180°, therefore
m∠DBC + 90° + α = 180°
m∠DBC = 90° - α
Again, for the same reason,
m∠DCB + m∠DBC + 90° = 180°
m∠DCB + 90° - α + 90° = 180°
m∠DCB = α
For the same reason,
m∠ACD + 90° + α = 180°
m∠ACD = 90° - α
m∠ADC = 90° (by definition)
m∠CDB = 90° (by definition)
Answer:
m∠DBC = 90° - α
m∠DCB = α
m∠CDB = 90°
m∠ACD = 90° - α
m∠ADC = 90°
Jack has twelve coins in his pocket made up of dimes and quarters. he has a total value of $1.95. how many of each are there
Answers
5 quarters = $1.25
7 dimes = $0.70
Total: 12 coins = $1.95
Please help me. Thank you.
Answers
3m + 20 + 5m = 180
8m + 20 = 180
8m = 160
m = 20
Then 3(20) +20 = 80 because of vertical angles.
The second one is 15 because of vertical angles. 2*115 = 230. 50*50 = 100. Add these up and you get 330. This leaves 30 missing degrees among the two remaining angles. Since the two remaining angles are congruent because they are vertical, you can divide 30 by 2 to get 15.
Sarah said that 0.00001 is bigger than 0.001 because the first number has more digits to the right of the decimal point. Is Sarah correct? Explain your thinking using negative powers of 10 and the number line
Answers
The number 0.001 is greater than the number 0.00001. She is incorrect.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Sarah said that 0.00001 is bigger than 0.001 because the first number has more digits to the right of the decimal point. She is incorrect.
0.001 > 0.00001
Because the number 0.001 is greater than the number 0.00001.
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Kim is drawing a map of the different schools in her school district.she knows that her middle school is 10.6 miles away from the middle school that her best friend attends.if every 2 inches on the map represents 5 miles, how far apart will the two schools be on the map,to the nearest tenth of an inch
Answers
10.6/5 = 2.12
that equation represents how many miles away they are now we mulitply
2.12x 2 to find a number of inches 4.24
Answer:
4.24 inches.
Step-by-step explanation:
In the map,
2 inches represents 5 miles,
Thus, we can write,
[tex]5\text{ miles}=2\text{ inches}[/tex]
[tex]1\text{ mile}=\frac{2}{5}\text{ inches}-----(1)[/tex]
Since, the actual distance between the two schools is 10.6 miles.
Multiplying both sides by 10.6 in equation (1),
[tex]10.6\text{ miles}=10.6\times \frac{2}{5}=\frac{21.2}{5}=4.24\text{ inches}[/tex]
Hence, the distance between the two schools in the map is 4.24 inches.
2 to determine the formula of a new substance one of the first steps is to find the
Answers
am i correct ? geometry problem
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A pack of cinnamon scented pancils sells for $7.00.What is the sales tax rate if the total cost of the pencils is $7.49?
Answers
The amount of sales tax rate on the scented pencils will be equal to 7%.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given information in the question,
Price of scented pencils = $7
Price of pencils after-tax = $7.49
Then, the percentage of tax on the pencils will be,
= (7.49 - 7)/7 × 100
= 0.07 × 100
= 7%
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The lengths of the sides of a triangle are in the extended ratio 5 : 7 : 10. The perimeter of the triangle is 88cm. What are the lengths of the sides?
Answers
5=5x4 which is 20
7=7x4 which is 28
10=10x4 which is 40 the answer is 20 cm, 28 cm, and 40 cm.
5=5x4=20
7=7x4=28
10=10x4=40
this is how u get ur answers
Hope this helps best of luck my friend :3
Geometry help please?
4 questions.
Thanks!
Answers
Statement Reasons
m∠ABD + m∠DBC = m∠ABC Angle addition postulate
60° + 40° = m∠ABC Substitution Property of equality
100° = m∠ABC Simplpifying
∠ABC is an obtuse angle Definition of obtuse angle
----------------------------------------------------------------------------------------------------------------
Question 2:
Statement Reasons
AC = BD Given
AC = BC + BD Segment addition postulate
AB + BC = BC + CD Addition property of equality
----------------------------------------------------------------------------------------------------------------
Question 3:
Angle congruence postulate
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Question 4:
Segment congruence postulate
The equation ax=0 has only the solution x=0 because
Answers
Look at the following expression.
5(3x + 2)
Which of the answer choices below is NOT an equivalent expression?
A.15x + 10
B.10x + 15
C.5 ∙ 3x + 5 ∙ 2
D.5(2 + 3x)
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The number of CDs sold has decreased each year. The graph shows the number of CDs sold in a given year. (coordinate graph) Which is a reasonable inference for the number of CDs at month 4?
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Graph f(x)=34x+2. Use the line tool and select two points to graph the line.
Answers
we have
[tex]f(x)=\frac{3}{4}x+2[/tex]
To graph the linear equation find the intercepts
we know that
The x-intercept is the value of x when the value of the function is equal to zero
The y-intercept is the value of the function when the value of x is equal to zero
so
Find the y-intercept
for [tex]x=0[/tex]
[tex]f(x)=\frac{3}{4}*0+2=2[/tex]
the y-intercept is the point [tex](0,2)[/tex]
Find the x-intercept
for [tex]f(x)=0[/tex]
[tex]0=\frac{3}{4}x+2[/tex]
Multiply by [tex]4[/tex] both sides
[tex]0=3x+8[/tex]
[tex]x=-\frac{8}{3}=-2.667[/tex]
the x-intercept is the point [tex](-2.667,0)[/tex]
Plot the intercepts to graph the line
The answer in the attached figure
Answer:
the answer is (-2,0) and (0, 2)
Good luck!
What is the value of x in the equation 2x + 3y = 36, when y = 6
Answers
2x+3y=36
y=6
2x +3(6) = 36
2x +18 =36
2x = 18
x = 9
Answer:
The value of the provide expression is 9.
Step-by-step explanation:
Consider the provided expression.
[tex]2x + 3y = 36 [/tex]
We need to find the value of the expression, for x when y=6
Substitute the respective values in the provided expression.
[tex]2x + 3(6) = 36 [/tex]
[tex]2x + 18 = 36 [/tex]
[tex]2x= 36-18 [/tex]
[tex]2x= 18 [/tex]
[tex]x= 9 [/tex]
Hence, the value of the provide expression is 9.
Suppose that the distance D feet that a car travels in t seconds is given by d(t)=2t^2. Calculate the average speed (average rate of change.) in feet per second from t=5 to t=9. (An exact number.)
Answers
The average rate of change is calculated by the formula: d(t2) - d(t1) / t2 - t1
So plug in 5 as t1 and 9 as t2.
d(9) - d(5) / 9 - 5 =
(2×81) - (2×25) / 9 - 5 =
162 - 50 / 4 =
112 / 4 = 28
The average speed is 28 feet.
A rate of change is a rate that describes how one quantity changes in relation to another quantity, then d(t)=2t^2 is given, 28 feet is average speed in feet per second from t=5 to t=9.
What is Rate of change?A rate of change is a rate that describes how one quantity changes in relation to another quantity.
d(t)=2t^2 is given, we need to find average speed in feet per second from t=5 to t=9.
d(t)=2t^2.
The average rate of change is calculated by the formula: d(t2) - d(t1) / t2 - t1
So plug in 5 as t1 and 9 as t2.
d(9) - d(5) / 9 - 5 =
(2×81) - (2×25) / 9 - 5 =
162 - 50 / 4 =
112 / 4 = 28
Therefore the average speed is 28 feet.
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ABCD is a kite, find the length of BD
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A. 8
B. 16
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Answers
Answer:
y = 4x − 3
Step-by-step explanation:
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Step-by-step explanation:
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Answers
200 + 150 + 250 + 260 + 285 + 380 + 200 + 225 + 200 + 250 + 220 + 150 = 2770
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