Logarithms Questions with solutions

The log questions for your practice with solutions to help you to improve problem-solving skill on logarithms.

Evaluate $\dfrac{1}{\log_{2}{30}}$ $+$ $\dfrac{1}{\log_{3}{30}}$ $+$ $\dfrac{1}{\log_{5}{30}}$

Solve $\log_{3}{\big(5+4\log_{3}{(x-1)}\big)}$ $\,=\,$ $2$

Evaluate $\log{\dfrac{x^2}{yz}}$ $+$ $\log{\dfrac{y^2}{zx}}$ $+$ $\log{\dfrac{z^2}{xy}}$

Solve $\log_{3}{(5x-2)}$ $-$ $2\log_{3}{\sqrt{3x+1}}$ $\,=\,$ $1$ $-$ $\log_{3}{4}$

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

Solve $2\log_{x}{a}$ $+$ $\log_{ax}{a}$ $+$ $3\log_{a^2x}{a}$ $\,=\,$ $0$

Solve $x$ $+$ $\log{(1+2^x)}$ $=$ $x\log{5}$ $+$ $\log{6}$

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

Solve $\log_{5}{x}+\log_{x}{5}$ $\,=\,$ $\dfrac{5}{2}$

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

Solve $\dfrac{\log{(\sqrt{x+1}+1)}}{\log{\sqrt[\Large 3]{x-40}}}$ $\,=\,$ $3$

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

Log Problems' Levels

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Basic Problems

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Advanced Problems

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Difficult Problems

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Worksheets

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Logarithm Expressions

The log questions on expressions with solutions to know how to evaluate logarithmic expressions.

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Logarithm Equations

The log questions on equations with solutions to know how to solve the logarithmic equations.

tough logarithm problems

Logarithm Inequalities

The log questions on inequations with solutions to know how to solve the logarithmic inequalities.

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