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Question 1

Expand $\log_3(27x^2)$ .

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Question 2

Expand $\ln\bigl(\frac{e^3x}{\sqrt{y}}\bigr)$ .

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Question 3

Expand $\log_7\left(\frac{\sqrt{xy}}{z^3}\right)$ .

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Question 4

Solve $2+\log_{4}(x)=\ln(x)$ for $x>0$ .

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Question 5

Express $\log_a(b)$ in terms of natural logarithms.

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Question 6

Solve the following equation.

Solve $\ln(x^2-1)-\ln(x+1)=\ln(2)$ for $x$ . [4 marks]

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Question 7

Evaluate logarithmic expressions using change of base rules.

Evaluate $\log_4(32)$ by rewriting in base 2. [3 marks]

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Question 8

Solve $\log_5(x)+\log_5(x-4)=1$ for $x$ .

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Question 9

Solve the logarithmic equation.

Solve $\log_{3}(2x-1)=2+\log_{3}(x+1)$ for $x$ .

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Question 10

Condense $4+\log_5(x)-2\log_5(y)$ into one logarithm.

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Question 11

Express $\log_2(x)+3\log_2(y)-\frac{1}{2}\log_2(z)$ as a single logarithm.

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Question 12

Solve $\log_2(x^2 - 4) = 3$ for $x$ .

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Question Type 10: Summarizing laws of logarithms Exercises