Free Printable Expanding and Condensing Logs

1.

If $A=\pi r^2$ , log A equals

a)

$2\log\pi+\log r$

b)

$\log\pi+2\log r$

c)

$2\log\pi+2\log r$

d)

$2\pi\log r$

2.

$L=\frac{x^2}{k}$ , then log L is equal to

If

a)

$2\log\ \frac{x}{k}$

b)

$2\left(\log x-\log k\right)$

c)

$2\log x-\log k$

d)

$\frac{2\log x}{\log k}$

3.

If $x=\left(8^2\right)\left(\sqrt{5}\right)$ , which expression is equivalent to log x?

a)

$2\log8+2\log5$

b)

$2\left(\log8+\frac{1}{2}\log5\right)$

c)

$2\log8+\frac{1}{2}\log5$

d)

$\left(2\log8\right)\left(\frac{1}{3}\log5\right)$

4.

$\log\ \frac{\sqrt{xy\ }}{z}$ is equal to which of the following?

a)

$\frac{1}{2}\log x+\frac{1}{2}\log y-\log z$

b)

$\frac{1}{2}\log x+\log y-\log z$

c)

$\frac{1}{2}\left(\log x+\log y-\log z\right)$

d)

$\frac{\frac{1}{2}\log xy}{\log z}$

5.

If $x=\frac{a\sqrt{b}}{c}$ , then what does $\log_{10}x$ equal?

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6.

If $x=\frac{8\left(5\right)^{\frac{1}{3}}}{21}$ , represent $\log_bx$ in expanded form

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7.

$N=\frac{\left(x^2y\right)^{\frac{1}{4}}}{z}$

Express log N in terms of log x, log y and log z:

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8.

If $\log x=2\log a-\left(3\log b+\frac{1}{2}\log\ d\right)$ , which expression is equivalent to x?

a)

$a^2b^3c^{\frac{1}{2}}$

b)

$\frac{a^2}{b^3\sqrt{d}}$

c)

$\frac{a^2}{\sqrt{b^3d}}$

d)

$\frac{a^2b^3}{\sqrt{d}}$

9.

$2\log_5m+\log_5n$

write as a single logarithm:

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10.

$\frac{1}{2}\log m-\log n$ Write as a single logarithm

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Expanding and Condensing Logs

Total questions: 10

Worksheet time: 3hrs 30mins

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