Free Printable Properties of Logarithms

1.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

2.

Write in exponential form: $\log_{14}196=2$

a)

$14^2=196$

b)

$2^{14}=196$

c)

$196^2=14$

d)

$2^{196}=14$

3.

Expand $\log_b\left(xy\right)$

a)

$\log_bx+\log_by$

b)

$\log_bx-\log_by$

c)

$\log_bx*\log_by$

d)

$\frac{\log_bx}{\log_by}$

4.

Expand: $\log_b\left(\frac{x}{y}\right)$

a)

$\log_bx-\log_by$

b)

$\log_bx+\log_by$

c)

$\log_bx*\log_by$

d)

$\frac{\log_bx}{\log_by}$

5.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

6.

Write the expression as a single logarithm. Then simplify if possible.

log 6 - log 3 + 2 log 7

a)

log 98

b)

log 78

c)

log 56

d)

log 45

7.

Simplify: $\log_73+\log_76$

a)

$\log_79$

b)

$\log_7\left(\frac{1}{2}\right)$

c)

$\log_718$

d)

$\log_7729$

8.

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

a)

$\log_49$

b)

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

c)

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

d)

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

9.

Simplify: $2\log_2x-\log_2\left(x+3\right)$

a)

$\log_2\left(x^3+3x^2\right)$

b)

$\log_2\left(2x^2+6x\right)$

c)

$\log_2\left(\frac{x^2}{x+3}\right)$

d)

$\log_2\left(\frac{2x}{x+3}\right)$

10.

$\log_6\left(\frac{5x^3}{y}\right)$

Expand .

a)

$\log_65x^3-\log_6y$

b)

$\log_65+\log_6x^3-\log_6y$

c)

$\log_65+3\log_6x-\log_6y$

Properties of Logarithms

Total questions: 10

Worksheet time: 13mins

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