Computing logarithms

Statement

Compute $\log_5 125$, $\log_2 \tfrac{1}{8}$, $\log_3 \sqrt[4]{27}$.

Solution

Each time one looks for the exponent to which the base must be raised to obtain the argument.

• $\log_5 125 = 3$, because $5^3 = 125$.
• $\log_2 \tfrac{1}{8} = -3$, because $2^{-3} = \tfrac{1}{8}$.
• $\log_3 \sqrt[4]{27} = \log_3 27^{1/4} = \log_3 3^{3/4} = \tfrac{3}{4}$.

Results: $\boxed{3,\ -3,\ \tfrac{3}{4}}$.

Links

Topics: Logarithmic function
Concepts: Logarithm
Functions: Logarithmic function
Skills: Calculate
Exercise type: Calculating expressions