Question Type 10: Summarizing laws of logarithms Exercises

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

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

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

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

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

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

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

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

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

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

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

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