Rewrite rewrite in exponential form. log ⁡ 1 2 16 = − 4 \log_{\frac{1}{2}}16=-4 lo g 2 1 1 6 = − 4

( 1 2 ) − 4 = 16 \left(\frac{1}{2}\right)^{-4}=16 ( 2 1 ) − 4 = 1 6

( 1 2 ) 16 = − 4 \left(\frac{1}{2}\right)^{16}=-4 ( 2 1 ) 1 6 = − 4

1 6 1 2 = − 4 16^{\frac{1}{2}}=-4 1 6 2 1 = − 4

− 4 1 2 = 16 -4^{\frac{1}{2}}=16 − 4 2 1 = 1 6

Rewrite in logarithmic form. 1 6 − 1 = 1 16 16^{-1}=\frac{1}{16} 1 6 − 1 = 1 6 1

log ⁡ 16 ( 1 16 ) = − 1 \log_{16}\left(\frac{1}{16}\right)=-1 lo g 1 6 ( 1 6 1 ) = − 1

log ⁡ 16 ( − 1 ) = 1 16 \log_{16}\left(-1\right)=\frac{1}{16} lo g 1 6 ( − 1 ) = 1 6 1

log ⁡ − 1 ( 1 16 ) = 16 \log_{-1}\left(\frac{1}{16}\right)=16 lo g − 1 ( 1 6 1 ) = 1 6

log ⁡ 1 16 ( − 1 ) = 16 \log_{\frac{1}{16}}\left(-1\right)=16 lo g 1 6 1 ( − 1 ) = 1 6

Rewrite in logarithmic form. 12 5 2 3 = 25 125^{\frac{2}{3}}=25 1 2 5 3 2 = 2 5

log ⁡ 125 ( 25 ) = 2 3 \log_{125}\left(25\right)=\frac{2}{3} lo g 1 2 5 ( 2 5 ) = 3 2

log ⁡ 2 3 125 = 25 \log_{\frac{2}{3}}125=25 lo g 3 2 1 2 5 = 2 5

log ⁡ 25 125 = 2 3 \log_{25}125=\frac{2}{3} lo g 2 5 1 2 5 = 3 2

Find the inverse of the function. y = 0. 3 x y=0.3^x y = 0 . 3 x

y = log ⁡ 0.3 x y=\log_{0.3}x y = lo g 0 . 3 x

x = log ⁡ 0.3 y x=\log_{0.3}y x = lo g 0 . 3 y

x = log ⁡ y 0.3 x=\log_y0.3 x = lo g y 0 . 3

y = log ⁡ x 0.3 y=\log_x0.3 y = lo g x 0 . 3

Find the inverse of the function. y = ln ⁡ ( x − 1 ) y=\ln\left(x-1\right) y = ln ( x − 1 )

y = e x + 1 y=e^x+1 y = e x + 1

y = e x + 1 y=e^{x+1} y = e x + 1

y = e x − 1 y=e^{x-1} y = e x − 1

y = e x − 1 y=e^x-1 y = e x − 1

Find the inverse of the function. y = e 3 x y=e^{3x} y = e 3 x

y = 1 3 ln ⁡ x y=\frac{1}{3}\ln x y = 3 1 ln x

y = 3 ln ⁡ x y=3\ln x y = 3 ln x

y = ln ⁡ ( 1 3 x ) y=\ln\left(\frac{1}{3}x\right) y = ln ( 3 1 x )

y = ln ⁡ 3 x y=\ln3x y = ln 3 x

Find the inverse of the function. y = e 3 x y=e^{3x} y = e 3 x

y = 1 3 ln ⁡ x y=\frac{1}{3}\ln x y = 3 1 ln x

y = 3 ln ⁡ x y=3\ln x y = 3 ln x

y = ln ⁡ ( 1 3 x ) y=\ln\left(\frac{1}{3}x\right) y = ln ( 3 1 x )

y = ln ⁡ 3 x y=\ln3x y = ln 3 x

Algebra 7.3 - Logarithms and Logarithmic Functions

Quiz

•

Mathematics

•

11th Grade

•

Practice Problem

•

Medium

•

CCSS

HSF.BF.B.5, HSF-BF.B.4A

Standards-aligned

Eric Hoffman

Used 53+ times

FREE Resource

15 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Rewrite in logarithmic form.
$\log_39=2$

$9^3=2$

$9^2=3$

$3^2=9$

$2^3=9$

Tags

CCSS.HSF.BF.B.5

2.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Rewrite in exponential form.
$\log_61=0$

$6^1=0$

$6^0=1$

$1^0=6$

$0^1=6$

Tags

CCSS.HSF.BF.B.5

3.

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

Rewrite rewrite in exponential form.
$\log_{\frac{1}{2}}16=-4$

$\left(\frac{1}{2}\right)^{16}=-4$

$16^{\frac{1}{2}}=-4$

$-4^{\frac{1}{2}}=16$

$\left(\frac{1}{2}\right)^{-4}=16$

Tags

CCSS.HSF.BF.B.5

4.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$6^2=36$
Rewrite in logarithmic form.

$\log_26=36$

$\log_{36}6=2$

$\log_636=2$

Tags

CCSS.HSF.BF.B.5

5.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Rewrite in logarithmic form.
$16^{-1}=\frac{1}{16}$

$\log_{16}\left(-1\right)=\frac{1}{16}$

$\log_{16}\left(\frac{1}{16}\right)=-1$

$\log_{-1}\left(\frac{1}{16}\right)=16$

$\log_{\frac{1}{16}}\left(-1\right)=16$

Tags

CCSS.HSF.BF.B.5

6.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Rewrite in logarithmic form.
$125^{\frac{2}{3}}=25$

$\log_{\frac{2}{3}}125=25$

$\log_{125}\left(25\right)=\frac{2}{3}$

$\log_{25}125=\frac{2}{3}$

Tags

CCSS.HSF.BF.B.5

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Evaluate the logarithm.
$\log_381$

1/4

4

-4

-1/4

Tags

CCSS.HSF.BF.B.5

8.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Evaluate the logarithm.
$\log_33$

0

1

-1

3

Tags

CCSS.HSF.BF.B.5

9.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Evaluate the logarithm.
$\log_5\left(\frac{1}{625}\right)$

4

1/4

-4

-1/4

Tags

CCSS.HSF.BF.B.5

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Evaluate the logarithm.
$\log_40.25$

1

-1

0

Tags

CCSS.HSF.BF.B.5

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Algebra 7.3 - Logarithms and Logarithmic Functions

15 questions

Rewrite in logarithmic form. log⁡39=2\log_39=2log3​9=2

Rewrite in exponential form. log⁡61=0\log_61=0log6​1=0

Rewrite rewrite in exponential form. log⁡1216=−4\log_{\frac{1}{2}}16=-4log21​​16=−4

62=366^2=3662=36 Rewrite in logarithmic form.

Rewrite in logarithmic form. 16−1=11616^{-1}=\frac{1}{16}16−1=161​

Rewrite in logarithmic form. 12523=25125^{\frac{2}{3}}=2512532​=25

Evaluate the logarithm. log⁡381\log_381log3​81

Evaluate the logarithm. log⁡33\log_33log3​3

Evaluate the logarithm. log⁡5(1625)\log_5\left(\frac{1}{625}\right)log5​(6251​)

Evaluate the logarithm. log⁡40.25\log_40.25log4​0.25

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Rewrite in logarithmic form.
$\log_39=2$

Rewrite in exponential form.
$\log_61=0$

Rewrite rewrite in exponential form.
$\log_{\frac{1}{2}}16=-4$

$6^2=36$
Rewrite in logarithmic form.

Rewrite in logarithmic form.
$16^{-1}=\frac{1}{16}$

Rewrite in logarithmic form.
$125^{\frac{2}{3}}=25$

Evaluate the logarithm.
$\log_381$

Evaluate the logarithm.
$\log_33$

Evaluate the logarithm.
$\log_5\left(\frac{1}{625}\right)$

Evaluate the logarithm.
$\log_40.25$