Properties of Logarithms

Authored by Tiffany Cooper

Mathematics

9th - 12th Grade

CCSS covered

Used 7+ times

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12 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which equation is equivalent to the equation below?
$7^x=24$

$\log_7x=24$

$\log_x7=24$

$\log_{24}7=x$

$\log_724=x$

Solve for x. Enter your answer as a fraction if possible.
$\log x=-3$

(a)

Evaluate.
$\log_2\frac{1}{32}$

(a)

FILL IN THE BLANKS QUESTION

1 min • 1 pt

Evaluate.
$\log_{16}4$

(a)

FILL IN THE BLANKS QUESTION

1 min • 1 pt

Evaluate.
$\log_61$

(a)

Evaluate using the Change of Base formula. Round to the nearest hundredth if possible.
$\log_584$

(a)

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Simplify the logarithm.
$\log_{10}5+\log_{10}x$

$\log_{10}\left(5+x\right)$

$\log_{10}\left(5x\right)$

$\log_{10}\left(5^x\right)$

$\log_{10}\left(5-x\right)$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Simplify the logarithm.
$\log_{10}30-\log_{10}10$

$\log40$

$\log20$

$\log300$

$\log3$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Expand the logarithm.
$\log_3\left(2y\right)$

$\log_32-\log_3y$

$\log2+\log y$

$2\log_3y$

$\log_3y+\log_32$

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Expand the logarithm.
$\log\left(\frac{7}{z}\right)$

$\log7+\log z$

$\log7-\log z$

$\log\left(7z\right)$

$\log\left(7^z\right)$

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Properties of Logarithms

Which equation is equivalent to the equation below? 7x=247^x=247x=24

Solve for x. Enter your answer as a fraction if possible. log⁡x=−3\log x=-3logx=−3 (a)

Evaluate. log⁡2132\log_2\frac{1}{32}log2​321​ (a)

Evaluate. log⁡164\log_{16}4log16​4 (a)

Evaluate. log⁡61\log_61log6​1 (a)

Evaluate using the Change of Base formula. Round to the nearest hundredth if possible. log⁡584\log_584log5​84 (a)

Simplify the logarithm. log⁡105+log⁡10x\log_{10}5+\log_{10}xlog10​5+log10​x

Simplify the logarithm. log⁡1030−log⁡1010\log_{10}30-\log_{10}10log10​30−log10​10

Expand the logarithm. log⁡3(2y)\log_3\left(2y\right)log3​(2y)

Expand the logarithm. log⁡(7z)\log\left(\frac{7}{z}\right)log(z7​)

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Which equation is equivalent to the equation below?
$7^x=24$

Solve for x. Enter your answer as a fraction if possible.
$\log x=-3$

(a)

Evaluate.
$\log_2\frac{1}{32}$

(a)

Evaluate.
$\log_{16}4$

(a)

Evaluate.
$\log_61$

(a)

Evaluate using the Change of Base formula. Round to the nearest hundredth if possible.
$\log_584$

(a)

Simplify the logarithm.
$\log_{10}5+\log_{10}x$

Simplify the logarithm.
$\log_{10}30-\log_{10}10$

Expand the logarithm.
$\log_3\left(2y\right)$

Expand the logarithm.
$\log\left(\frac{7}{z}\right)$