Logarithm problems and solutions

Expressions

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.

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

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

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