The list of questions on the logarithmic expressions in arithmetic form with solutions to learn how to evaluate the arithmetic logarithm expressions by using the logarithm rules.

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

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