MIXED REVIEW: Exponential and Logarithmic Equations

Authored by Gayle Herrington

Mathematics

9th - 12th Grade

CCSS covered

Used 5+ times

MIXED REVIEW: Exponential and Logarithmic Equations

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41 questions

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Rewrite 3⁴ = 81 in logarithmic form.

log₃(4 ) = 81

log₈₁ ( 3 ) = 4

log₃( 81 ) = 4

log₄ (81 ) = 3

Write in exponential form.
log₂(32) = 5

2^-5 = 32

2³² = 5

2⁵ = 32

32⁵ = 2

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

2^-3 = ¹/₈

2^1/8= -3

-3² = ¹/₈

-3^1/8 = 2

log₄( 1 ) =

DNE

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Condense: $\log_4\left(x+4\right)-\log_4\left(x-5\right)$

$\log_49$

$\log_4\left(2x-1\right)$

$\log_4\left(x^2-x-20\right)$

$\log_4\left(\frac{x+4}{x-5}\right)$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Condense: $\log_25+\log_2x$

$\log_2x^5$

$\log_2\ \frac{5}{x}$

$\log_2\ \frac{x}{5}$

$\log_25x$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Condense: $7\log v\ +\ 3\log w$

$\log\ \frac{v^7}{w^3}$

$\log21vw$

$\log v^7w^3$

$10\log\ \frac{v}{w}$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Expand the logarithm expression
log $\left(\frac{5x}{4y}\right)$

log 5x + log 4y

log 5x - 4log y

(log 5 + log x) - (log 4 + logy)

5log x - 4 logy

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Continue solving for x. Which is the correct "step 2"?

$64=x^3$

$64^3=x$

$x^{64}=3$

$3^{64}=x$

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$4\log_2\left(2x+24\right)-17=-9$
Once you have isolated the log in the equation, what would be the next step?

log both sides

rewrite as an exponential

nothing, you would not be able to solve it

divide both sides by 2

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MIXED REVIEW: Exponential and Logarithmic Equations

Rewrite 34 = 81 in logarithmic form.

Write in exponential form.log2 (32) = 5

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

log4 ( 1 ) =

Condense: log⁡4(x+4)−log⁡4(x−5)\log_4\left(x+4\right)-\log_4\left(x-5\right)log4​(x+4)−log4​(x−5)

Condense: log⁡25+log⁡2x\log_25+\log_2xlog2​5+log2​x

Condense: 7log⁡v + 3log⁡w7\log v\ +\ 3\log w7logv + 3logw

Expand the logarithm expressionlog (5x4y)\left(\frac{5x}{4y}\right)(4y5x​)

Continue solving for x. Which is the correct "step 2"?

4log⁡2(2x+24)−17=−94\log_2\left(2x+24\right)-17=-94log2​(2x+24)−17=−9 Once you have isolated the log in the equation, what would be the next step?

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Rewrite 3⁴ = 81 in logarithmic form.

Write in exponential form.
log₂(32) = 5

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

log₄( 1 ) =

Condense: $\log_4\left(x+4\right)-\log_4\left(x-5\right)$

Condense: $\log_25+\log_2x$

Condense: $7\log v\ +\ 3\log w$

Expand the logarithm expression
log $\left(\frac{5x}{4y}\right)$

$4\log_2\left(2x+24\right)-17=-9$
Once you have isolated the log in the equation, what would be the next step?