# Logarithms Questions with solutions

Once you learn the logarithmic rules clearly, you are ready to use them as formulas in log questions. The logarithm practice problems worksheet is given here with answers and the variety of examples for students who study the logarithms and also the solutions to learn how to find the logarithms by the log properties in the problems.

### Expressions

$(1).\,\,$ Evaluate $\log_{5}{7^{\displaystyle -3\log_{7}{5}}}$

$(2).\,\,$ $\log{\Big(\dfrac{x^2}{yz}\Big)}$ $+$ $\log{\Big(\dfrac{y^2}{zx}\Big)}$ $+$ $\log{\Big(\dfrac{z^2}{xy}\Big)}$

$(3).\,\,$ Evaluate $\log_{\sqrt{2}}{\sqrt{2\sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}}}}$

List of the logarithmic expressions problems with solutions to learn how to evaluate them by simplification.

### Equations

List of the logarithmic equations problems with solutions to learn how to solve the logarithm equations.

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

$(2).\,\,$ Evaluate $\dfrac{x}{y}+\dfrac{y}{x}$ if $\log{\Big(\dfrac{x+y}{3}\Big)}$ $\,=\,$ $\dfrac{1}{2}(\log{x}+\log{y})$

$(3).\,\,$ Solve $x$ $+$ $\log{(1+2^x)}$ $=$ $x\log{5}$ $+$ $\log{6}$

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