Question 1

Solve the equation. Give your answer to four decimal places. ${ } ^ { 227 } \mathrm { Th }$

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The answer of Solve the equation. Give your answer to...

Question 2

An isotope of thorium, ${ } ^ { 227 } \mathrm { Th }$ , has a half-life of 18.4 days. How long will it take for 77% of the sample to decompose?
 Please round the answer to the nearest tenth.

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The answer of An isotope of thorium, \({ } ^...

Question 3

Solve the equation. $6 ^ { 4 x } = \frac { 1 } { 216 }$ If there is more than one solution, separate your answers with commas.

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Question 4

Solve the equation. Give your answer to four decimal places. ${ } ^ { 227 } \mathrm { Th }$

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Question 5

Solve the following equation. $3 ^ { x ^ { 2 } - 2 x }= 27$ If there is more than one solution, separate your answers with commas.

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Question 6

Solve the equation. Give your answer to four decimal places. $13 ^ { x - 1 } = 3$ If there is more than one solution, separate your answers with commas.

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Question 7

Solve the equation. ${ } ^ { 227 } \mathrm { Th }$

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The answer of Solve the equation. \({ } ^ {...

Question 8

Solve: $\log ( x + 8 ) = 2 + \log x$

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The answer of Solve: \(\log ( x + 8 )...

Question 9

Solve: $\log _ { 3 } x + \log _ { 3 } ( x - 8 ) = 2$

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Question 10

Solve the equation. $\log ( x - 5 ) - \log ( x - 2 ) = \log \frac { 4 } { x }$ If there is more than one solution, separate your answers with commas.

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The answer of Solve the equation. \(\log ( x -...

Question 11

Solve: $3 ^ { 8 x - 1 } = \frac { 1 } { 27 }$

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Question 12

Solve the equation. $\log ( 4 - 3 x ) - \log ( x + 32 ) = 0$ If there is more than one solution, separate your answers with commas.

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The answer of Solve the equation. \(\log ( 4 -...

Question 13

Solve: $3 ^ { x ^ { 2 } - 3 x } = 81$

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Question 14

Solve the equation. $2 \log ( y + 2 ) = \log ( y + 2 ) - \log 11$ If there is more than one solution, separate your answers with commas.

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The answer of Solve the equation. \(2 \log ( y...

Question 15

Solve the equation. Give the exact answer in terms of ln . $e ^ { 2 t } = 7$

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Question 16

Solve the equation. Round answer to four decimal places. $7 ^ { x } = 14$

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Question 17

Solve: $\log \left( x ^ { 2 } - 1 \right) - \log ( x + 1 ) = 2$

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Question 18

Solve the equation. Give the exact answer. $\ln x = 3$

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Question 19

Solve: $\log _ { 3 } 7 x - \log _ { 3 } 12 = 1$

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The answer of Solve: \(\log _ { 3 } 7...

Quiz 9: Exponential and Logarithmic Functions

Solve the equation. Give your answer to four decimal places. 227Th{ } ^ { 227 } \mathrm { Th }227Th

An isotope of thorium, 227Th{ } ^ { 227 } \mathrm { Th }227Th , has a half-life of 18.4 days. How long will it take for 77% of the sample to decompose? Please round the answer to the nearest tenth.

Solve the equation. 64x=12166 ^ { 4 x } = \frac { 1 } { 216 }64x=2161​ If there is more than one solution, separate your answers with commas.

Solve the equation. Give your answer to four decimal places. 227Th{ } ^ { 227 } \mathrm { Th }227Th

Solve the following equation. 3x2−2x=273 ^ { x ^ { 2 } - 2 x }= 273x2−2x=27 If there is more than one solution, separate your answers with commas.

Solve the equation. Give your answer to four decimal places. 13x−1=313 ^ { x - 1 } = 313x−1=3 If there is more than one solution, separate your answers with commas.

Solve the equation. 227Th{ } ^ { 227 } \mathrm { Th }227Th

Solve: log⁡(x+8)=2+log⁡x\log ( x + 8 ) = 2 + \log xlog(x+8)=2+logx

Solve: log⁡3x+log⁡3(x−8)=2\log _ { 3 } x + \log _ { 3 } ( x - 8 ) = 2log3​x+log3​(x−8)=2

Solve the equation. log⁡(x−5)−log⁡(x−2)=log⁡4x\log ( x - 5 ) - \log ( x - 2 ) = \log \frac { 4 } { x }log(x−5)−log(x−2)=logx4​ If there is more than one solution, separate your answers with commas.

Solve: 38x−1=1273 ^ { 8 x - 1 } = \frac { 1 } { 27 }38x−1=271​

Solve the equation. log⁡(4−3x)−log⁡(x+32)=0\log ( 4 - 3 x ) - \log ( x + 32 ) = 0log(4−3x)−log(x+32)=0 If there is more than one solution, separate your answers with commas.

Solve: 3x2−3x=813 ^ { x ^ { 2 } - 3 x } = 813x2−3x=81

Solve the equation. 2log⁡(y+2)=log⁡(y+2)−log⁡112 \log ( y + 2 ) = \log ( y + 2 ) - \log 112log(y+2)=log(y+2)−log11 If there is more than one solution, separate your answers with commas.

Solve the equation. Give the exact answer in terms of ln . e2t=7e ^ { 2 t } = 7e2t=7

Solve the equation. Round answer to four decimal places. 7x=147 ^ { x } = 147x=14

Solve: log⁡(x2−1)−log⁡(x+1)=2\log \left( x ^ { 2 } - 1 \right) - \log ( x + 1 ) = 2log(x2−1)−log(x+1)=2

Solve the equation. Give the exact answer. ln⁡x=3\ln x = 3lnx=3

Solve: log⁡37x−log⁡312=1\log _ { 3 } 7 x - \log _ { 3 } 12 = 1log3​7x−log3​12=1

Solve the equation. Give your answer to four decimal places. ${ } ^ { 227 } \mathrm { Th }$

An isotope of thorium, ${ } ^ { 227 } \mathrm { Th }$ , has a half-life of 18.4 days. How long will it take for 77% of the sample to decompose? Please round the answer to the nearest tenth.

Solve the equation. $6 ^ { 4 x } = \frac { 1 } { 216 }$ If there is more than one solution, separate your answers with commas.

Solve the equation. Give your answer to four decimal places. ${ } ^ { 227 } \mathrm { Th }$

Solve the following equation. $3 ^ { x ^ { 2 } - 2 x }= 27$ If there is more than one solution, separate your answers with commas.

Solve the equation. Give your answer to four decimal places. $13 ^ { x - 1 } = 3$ If there is more than one solution, separate your answers with commas.

Solve the equation. ${ } ^ { 227 } \mathrm { Th }$

Solve: $\log ( x + 8 ) = 2 + \log x$

Solve: $\log _ { 3 } x + \log _ { 3 } ( x - 8 ) = 2$

Solve the equation. $\log ( x - 5 ) - \log ( x - 2 ) = \log \frac { 4 } { x }$ If there is more than one solution, separate your answers with commas.

Solve: $3 ^ { 8 x - 1 } = \frac { 1 } { 27 }$

Solve the equation. $\log ( 4 - 3 x ) - \log ( x + 32 ) = 0$ If there is more than one solution, separate your answers with commas.

Solve: $3 ^ { x ^ { 2 } - 3 x } = 81$

Solve the equation. $2 \log ( y + 2 ) = \log ( y + 2 ) - \log 11$ If there is more than one solution, separate your answers with commas.

Solve the equation. Give the exact answer in terms of ln . $e ^ { 2 t } = 7$

Solve the equation. Round answer to four decimal places. $7 ^ { x } = 14$

Solve: $\log \left( x ^ { 2 } - 1 \right) - \log ( x + 1 ) = 2$

Solve the equation. Give the exact answer. $\ln x = 3$

Solve: $\log _ { 3 } 7 x - \log _ { 3 } 12 = 1$