Free Printable Properties of Logs (NTI7)

1.

Condense: log₂6+log₂3=

a)

log₂18

b)

log₂2 = 1

c)

log₂3

d)

log₂9

2.

Write log_b(xy) as two logs

a)

log_bx+log_by

b)

log_bx-log_by

c)

log_bx*log_by

d)

log_bx/log_by

3.

Expand

a)

A

b)

B

c)

C

d)

D

4.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

5.

Write as a single log: $\log\left(12\right)+2\log\left(x\right)$

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

6.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

7.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

8.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

9.

Write the exponential equation as a logarithm
6³=216

a)

log₆(3) = 216

b)

log₃(6) = 216

c)

log₆(216)=3

d)

log₂₁₆(6)=3

10.

Change to Logarithmic Form:
12² = 144

a)

log₂ 144 = 12

b)

log₁₂ 144 = 2

c)

log ₁₂ 2 = 144

d)

log ₂ 12 = 144

11.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

12.

Change to Logarithmic Form:
5³ = 125

a)

log ₅ 125 = 3

b)

log₃125 = 5

c)

log ₅ 3 =125

d)

log₁₂₅ 3 = 5

13.

Expand the following logarithmic expression: $\log\left(\sqrt{\frac{x}{y}}\right)$

a)

$\log\left(x\right)-\log\left(y\right)$

b)

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

c)

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

d)

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

e)

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

14.

Condense the following logarithmic expression: $2\log\left(z\right)+\frac{1}{2}\log\left(x\right)$

a)

$\log\left(2z\cdot\frac{x}{2}\right)$

b)

$\log\left(z^2x^2\right)$

c)

$\log\left(z^2\cdot\sqrt{x}\right)$

d)

$\log\left(z^2+\sqrt{x}\right)$

15.

Rewrite in logarithmic form: $a^x=b$

a)

$\log_ax=b$

b)

$\log_ab=x$

c)

$\log_xa=b$

d)

$\log_ba=x_{ }$

Properties of Logs (NTI7)

Total questions: 15

Worksheet time: 4hrs 45mins

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