Logarithmic expressions in Arithmetic form Questions with solutions

The problems on logarithmic expressions in arithmetic form are excellent examples for beginners and new learners who want to build a strong foundation. To simplify numerical-based logarithmic expression questions, start by applying essential logarithm identities and follow our step-by-step solutions to strengthen your problem-solving skills. Now, complete the worksheet below on arithmetic form logarithmic expressions to understand how to evaluate and simplify each problem with confidence.

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