Question Type 1: Using logarithm laws to solve numerical expressions Exercises

Evaluate $(\log_{10}1000 - \log_{10}10) + \log_{10}5$.

Find the value of $3\log_5 25 - \log_5 125$.

Simplify and evaluate $\log_2 8 + \log_2 \tfrac{1}{4} - \log_2 2$.

Evaluate $(\,\log_3 81 + 2\log_3 3) - \log_3 9$.

Find the value of $(\log_2 3 + \log_2 6) - \log_2 9$.

Simplify $2\log_7 49 - \log_7 7 + \log_7 14$.

Simplify $\log_4 32 + \log_4 8 - 3\log_4 2$.

Compute $(\log_2 16 - \log_8 2) + \log_4 4$.

Simplify and evaluate $(\log_3 27 - \log_9 3) + \log_3 \sqrt{3}$.

Evaluate $2\log_3 9 + \log_9 3 - \log_3 \tfrac{1}{3}$.

Compute $(\log_8 64 + 2\log_4 2) - \log_2 16$.

Simplify $\log_5 125 - 2\log_{25} 5 + \log_5 \tfrac{1}{25}$.