Logarithmic expressions in Arithmetic form Questions with solutions

In logarithms, the expressions are appeared in arithmetic form in some log problems and they can be evaluated by simplifying the arithmetic-based log expressions with logarithmic identities. Simplifying the logarithm expressions in arithmetic form examples worksheet is given here for students practice with answers, and also solutions to learn how to evaluate the arithmetic form logarithmic expressions using the log rules by the simplification.

Evaluate $\log_{5}{7^{\displaystyle -3\log_{7}{5}}}$

Find $7\log_{2}{\bigg(\dfrac{16}{15}\bigg)}$ $+$ $5\log_{2}{\bigg(\dfrac{25}{24}\bigg)}$ $+$ $3\log_{2}{\bigg(\dfrac{81}{80}\bigg)}$

Evaluate $\log_{\sqrt{2}}{\sqrt{2\sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}}}}$

Find $\dfrac{\log_{4}{17}}{\log_{9}{23}}$ $-$ $\dfrac{\log_{2}{17}}{\log_{3}{23}}$

Evaluate $\log{2}$ $+$ $16\log{\Big(\dfrac{16}{15}\Big)}$ $+$ $12\log{\Big(\dfrac{25}{24}\Big)}$ $+$ $7\log{\Big(\dfrac{81}{80}\Big)}$

Evaluate $\dfrac{\log{\sqrt{27}}+\log{\sqrt{8}}-\log{\sqrt{125}}}{\log{6}-\log{5}}$