Question 1

Use the properties of logarithms to write each expression as a single logarithm.
-Write the expression $\log_3\frac{4x^2}{y+1}$ as the sum or difference of multiples of logarithms.

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Question 2

Find the exact value.
-$ln e^{-4}$

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-$ln e^{-4}$...

Question 3

Find the exact value.
-log 1000

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-log 1000...

Question 4

Find the exact value.
-Approximate logS1U1B13S1U1B0 21 to four decimal places.

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The answer of Find the exact value.
-Approximate logS1U1B13S1U1B0 21 to...

Question 5

Find the exact value.
-Solve: $\log_3 (x + 1) + \log_3 ( x + 3) = \log_3 3$ .

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The answer of Find the exact value.
-Solve: \(\log_3 (x +...

Question 6

For f ( x) = x - 9 and g(x) = 5 - xS1U1P12S1S1P0 , find (f - g)(x) and ( f $\circ$ g)(x)

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Question 7

Determine whether the function is one-to-one. If it is one-to-one, list the elements of its inverse {(3, -4), (4, 5), (6, -2), (2, 4), (9, -9)}

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Question 8

$f(x) = \sqrt[3]{x+1}$ is a one-to-one function. Find its inverse, and graph both on the same set of axes.

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Question 9

Solve fpr x: $2^{(7+3x)} = 4^{-1}$

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Question 10

Graph the exponential function $y = (1/3)^{-x} + 2$

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Question 11

The number of bacteria in a culture that initially contains 1200 bacteria grows at a rate of 6.9% per hour. How many bacteria are there after 10 hours? Use y = 1200(2.7)S1U1P10.069tS1S1P0 where t is time in hours

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Question 12

Solve for x: ln(x+2) = 3

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Question 13

Graph y = logS1U1B13S1U1B0x and its inverse on the same set of axes. Label any intercepts.

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Question 14

Write $\log_7\frac{x^5}{x^2-1}$ as a sum or difference of logarithms.

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The answer of Write $\log_7\frac{x^5}{x^2-1}$ as a sum or difference...

Question 15

Write $2 \log_6 4 - \log_6 8 + \log_6 5$ as the logarithm of a single expression.

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The answer of Write \(2 \log_6 4 - \log_6 8...

Question 16

Write $\frac13\log_5x + \frac14\log_5y - \frac15\log_5z$ as the logarithm of a single expression, assuming that x, y, and z are positive.

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The answer of Write $\frac13\log_5x + \frac14\log_5y - \frac15\log_5z$ as...

Question 17

If $\log_b 12 = 4.68 and \log_b 5 = -1.24 , find \log_b 120$ .

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Question 18

Approximate the value of logS1U1B14S1U1B0 925 to four decimal places.

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Question 19

Solve for x: $\log_{63}x = \frac12$

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Question 20

Solve for x: $\log(\frac{x-39}{x}) =2$

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The answer of Solve for x: $\log(\frac{x-39}{x}) =2$...

Quiz 9: Exponential and Logarithmic Functions

Use the properties of logarithms to write each expression as a single logarithm. -Write the expression $\log_3\frac{4x^2}{y+1}$ as the sum or difference of multiples of logarithms.

Find the exact value. - $ln e^{-4}$

Find the exact value. -log 1000

Find the exact value. -Approximate log₃ 21 to four decimal places.

Find the exact value. -Solve: $\log_3 (x + 1) + \log_3 ( x + 3) = \log_3 3$ .

For f ( x) = x - 9 and g(x) = 5 - x² , find (f - g)(x) and ( f $\circ$ g)(x)

Determine whether the function is one-to-one. If it is one-to-one, list the elements of its inverse {(3, -4), (4, 5), (6, -2), (2, 4), (9, -9)}

$f(x) = \sqrt[3]{x+1}$ is a one-to-one function. Find its inverse, and graph both on the same set of axes.

Solve fpr x: $2^{(7+3x)} = 4^{-1}$

Graph the exponential function $y = (1/3)^{-x} + 2$

The number of bacteria in a culture that initially contains 1200 bacteria grows at a rate of 6.9% per hour. How many bacteria are there after 10 hours? Use y = 1200(2.7)^0.069t where t is time in hours

Solve for x: ln(x+2) = 3

Graph y = log₃x and its inverse on the same set of axes. Label any intercepts.

Write $\log_7\frac{x^5}{x^2-1}$ as a sum or difference of logarithms.

Write $2 \log_6 4 - \log_6 8 + \log_6 5$ as the logarithm of a single expression.

Write $\frac13\log_5x + \frac14\log_5y - \frac15\log_5z$ as the logarithm of a single expression, assuming that x, y, and z are positive.

If $\log_b 12 = 4.68 and \log_b 5 = -1.24 , find \log_b 120$ .

Approximate the value of log₄ 925 to four decimal places.

Solve for x: $\log_{63}x = \frac12$

Solve for x: $\log(\frac{x-39}{x}) =2$

Quiz 9: Exponential and Logarithmic Functions

Use the properties of logarithms to write each expression as a single logarithm. -Write the expression log⁡34x2y+1\log_3\frac{4x^2}{y+1}log3​y+14x2​ as the sum or difference of multiples of logarithms.

Find the exact value. - lne−4ln e^{-4}lne−4

Find the exact value. -log 1000

Find the exact value. -Approximate log3 21 to four decimal places.

Find the exact value. -Solve: log⁡3(x+1)+log⁡3(x+3)=log⁡33\log_3 (x + 1) + \log_3 ( x + 3) = \log_3 3log3​(x+1)+log3​(x+3)=log3​3 .

For f ( x) = x - 9 and g(x) = 5 - x2 , find (f - g)(x) and ( f ∘\circ∘ g)(x)

Determine whether the function is one-to-one. If it is one-to-one, list the elements of its inverse {(3, -4), (4, 5), (6, -2), (2, 4), (9, -9)}

f(x)=x+13f(x) = \sqrt[3]{x+1}f(x)=3x+1​ is a one-to-one function. Find its inverse, and graph both on the same set of axes.

Solve fpr x: 2(7+3x)=4−12^{(7+3x)} = 4^{-1}2(7+3x)=4−1

Graph the exponential function y=(1/3)−x+2y = (1/3)^{-x} + 2y=(1/3)−x+2

The number of bacteria in a culture that initially contains 1200 bacteria grows at a rate of 6.9% per hour. How many bacteria are there after 10 hours? Use y = 1200(2.7)0.069t where t is time in hours

Solve for x: ln(x+2) = 3

Graph y = log3x and its inverse on the same set of axes. Label any intercepts.

Write log⁡7x5x2−1\log_7\frac{x^5}{x^2-1}log7​x2−1x5​ as a sum or difference of logarithms.

Write 2log⁡64−log⁡68+log⁡652 \log_6 4 - \log_6 8 + \log_6 52log6​4−log6​8+log6​5 as the logarithm of a single expression.

Write 13log⁡5x+14log⁡5y−15log⁡5z\frac13\log_5x + \frac14\log_5y - \frac15\log_5z31​log5​x+41​log5​y−51​log5​z as the logarithm of a single expression, assuming that x, y, and z are positive.

If log⁡b12=4.68andlog⁡b5=−1.24,findlog⁡b120\log_b 12 = 4.68 and \log_b 5 = -1.24 , find \log_b 120logb​12=4.68andlogb​5=−1.24,findlogb​120 .

Approximate the value of log4 925 to four decimal places.

Solve for x: log⁡63x=12\log_{63}x = \frac12log63​x=21​

Solve for x: log⁡(x−39x)=2\log(\frac{x-39}{x}) =2log(xx−39​)=2

Use the properties of logarithms to write each expression as a single logarithm. -Write the expression $\log_3\frac{4x^2}{y+1}$ as the sum or difference of multiples of logarithms.

Find the exact value. - $ln e^{-4}$

Find the exact value. -Approximate log₃ 21 to four decimal places.

Find the exact value. -Solve: $\log_3 (x + 1) + \log_3 ( x + 3) = \log_3 3$ .

For f ( x) = x - 9 and g(x) = 5 - x² , find (f - g)(x) and ( f $\circ$ g)(x)

$f(x) = \sqrt[3]{x+1}$ is a one-to-one function. Find its inverse, and graph both on the same set of axes.

Solve fpr x: $2^{(7+3x)} = 4^{-1}$

Graph the exponential function $y = (1/3)^{-x} + 2$

The number of bacteria in a culture that initially contains 1200 bacteria grows at a rate of 6.9% per hour. How many bacteria are there after 10 hours? Use y = 1200(2.7)^0.069t where t is time in hours

Graph y = log₃x and its inverse on the same set of axes. Label any intercepts.

Write $\log_7\frac{x^5}{x^2-1}$ as a sum or difference of logarithms.

Write $2 \log_6 4 - \log_6 8 + \log_6 5$ as the logarithm of a single expression.

Write $\frac13\log_5x + \frac14\log_5y - \frac15\log_5z$ as the logarithm of a single expression, assuming that x, y, and z are positive.

If $\log_b 12 = 4.68 and \log_b 5 = -1.24 , find \log_b 120$ .

Approximate the value of log₄ 925 to four decimal places.

Solve for x: $\log_{63}x = \frac12$

Solve for x: $\log(\frac{x-39}{x}) =2$