# Solving Logarithmic equations Questions with solutions

Solving the logarithmic equations in mathematics is another type of logarithmic problems. In fact, the log equations are solving for evaluating variables. For solving the logarithm equations, it is essential for everyone to have knowledge on fundamental operations of mathematics and also the rules of the logarithms.

Solve $\log_{5-x}{(x^2-2x+65)} \,=\, 2$

Solve $\log{7}$ $+$ $\log{(3x-2)}$ $=$ $\log{(x+3)}$ $+$ $1$

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

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

## Same Base

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

### Different Bases

$(1).\,\,$ Solve $\log_{2}{x}$ $+$ $\log_{4}{x}$ $+$ $\log_{16}{x}$ $\,=\,$ $7$

$(2).\,\,$ Solve $\log_{\large (2x+3)}{(6x^2+3x+21)}$ $\,=\,$ $4$ $-$ $\log_{\large (3x+7)}{(4x^2+12x+9)}$

The list of questions on solving the logarithmic equations with different bases and solutions to learn how to solve the log equation with different bases by the log laws.

$(1).\,\,$ Solve $\log_{\large 5}{(x)}+\log_{\large x}{(5)}$ $\,=\,$ $\dfrac{5}{2}$

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

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

The list of questions on quadratic form equation based logarithmic equations with solutions for you to learn how to solve quadratic equation form logarithmic equations in mathematics.

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