Solve for x using the same base method: 1 4 = 1 6 ( 2 x − 5 ) \frac{1}{4}=16^{\left(2x-5\right)} 4 1 = 1 6 ( 2 x − 5 )

− 11 4 -\frac{11}{4} − 4 1 1

log ⁡ 2 6 + log ⁡ 2 3 \log_26+\log_23 lo g 2 6 + lo g 2 3 Condense the expression into a single logarithm.

log ⁡ 2 18 \log_218 lo g 2 1 8

log ⁡ 2 16 − log ⁡ 2 4 \log_216-\log_24 lo g 2 1 6 − lo g 2 4 Condense the expression into a single logarithm. Simplify if possible.

log ⁡ 2 4 16 \log_24^{16} lo g 2 4 1 6

log ⁡ 2 64 \log_264 lo g 2 6 4

Log with a base "e" (log e ) is the same thing as...

Natural Logarithm base e (ln e )

Rewrite the exponential equation in logarithmic form. e x = 15 e^x=15 e x = 1 5

ln ⁡ 15 = x \ln15=x ln 1 5 = x

log ⁡ x = 15 \log x=15 lo g x = 1 5

ln ⁡ x = 15 \ln x=15 ln x = 1 5

log ⁡ 15 = x \log15=x lo g 1 5 = x

Solve for x. 3 e − 2 x + 4 = 10 3e^{-2x}+4=10 3 e − 2 x + 4 = 1 0

ln ⁡ 2 − 2 \frac{\ln2}{-2} − 2 ln 2

ln ⁡ ( 14 3 ) 3 \frac{\ln\left(\frac{14}{3}\right)}{3} 3 ln ( 3 1 4 )

ln ⁡ ( 14 3 ) − 2 \frac{\ln\left(\frac{14}{3}\right)}{-2} − 2 ln ( 3 1 4 )

ln ⁡ 2 3 \frac{\ln2}{3} 3 ln 2

Exponential and Logarithms Test Review

Authored by Tina Bergmann

Mathematics

10th - 12th Grade

CCSS covered

Used 15+ times

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31 questions

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MULTIPLE CHOICE QUESTION

10 mins • 1 pt

What is the inverse of an exponential function?

Exponential function

Power function

Logarithmic function

Base e function

Tags

CCSS.HSF-BF.B.4A

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Write in exponential form.
log₂32 = 5

2^-5 = 32

2³² = 5

2⁵ = 32

32⁵ = 2

Tags

CCSS.HSF.BF.B.5

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Write in exponential form.
log₂(¹/₈) = -3

2^-3 = ¹/₈

2^1/8= -3

-3² = ¹/₈

-3^1/8 = 2

Tags

CCSS.HSF.BF.B.5

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Write in logarithmic form.
2^-4 = ¹/₁₆

log₂(¹/₁₆) = -4

log_-4(¹/₁₆) = 2

log_-4 2 = ¹/₁₆

log₂(-4) = ¹/₁₆

Tags

CCSS.HSF.BF.B.5

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Write in logarithmic form.
5² = 25

log₅2 = 25

log₂25 = 5

log₅25 = 2

log₂₅5 = 2

Tags

CCSS.HSF.BF.B.5

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Solve for x using the same base method:
(-3)^x = (-3)¹³

-3

X+13

x-13

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Solve for x using the same base metod:
27^2x = 3^x-7

$-\frac{7}{3}$

-1

$-\frac{5}{7}$

-\frac{7}{5}

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Solve for x using the same base method:
$\frac{1}{4}=16^{\left(2x-5\right)}$

$-\frac{11}{4}$

$\frac{9}{4}$

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Evaluate the logarithm:
log₃81

$\frac{1}{4}$

-4

$-\frac{1}{4}$

10.

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Evaluate the logarithm:
$\log_6\left(\frac{1}{216}\right)$

$\frac{1}{3}$

$-\frac{1}{3}$

-3

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Exponential and Logarithms Test Review

What is the inverse of an exponential function?

Write in exponential form.log232 = 5

Write in exponential form.log2(1/8) = -3

Write in logarithmic form.2-4 = 1/16

Write in logarithmic form.52 = 25

Solve for x using the same base method:(-3)x = (-3)13

Solve for x using the same base metod:272x = 3x-7

Solve for x using the same base method: 14=16(2x−5)\frac{1}{4}=16^{\left(2x-5\right)}41​=16(2x−5)

Evaluate the logarithm: log381

Evaluate the logarithm: log⁡6(1216)\log_6\left(\frac{1}{216}\right)log6​(2161​)

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Discover more resources for Mathematics

Write in exponential form.
log₂32 = 5

Write in exponential form.
log₂(¹/₈) = -3

Write in logarithmic form.
2^-4 = ¹/₁₆

Write in logarithmic form.
5² = 25

Solve for x using the same base method:
(-3)^x = (-3)¹³

Solve for x using the same base metod:
27^2x = 3^x-7

Solve for x using the same base method:
$\frac{1}{4}=16^{\left(2x-5\right)}$

Evaluate the logarithm:
log₃81

Evaluate the logarithm:
$\log_6\left(\frac{1}{216}\right)$