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Logarithmic equations Problems and 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 $\log_{5}{(x)}+\log_{x}{(5)}$ $\,=\,$ $\dfrac{5}{2}$

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

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

Solve $\log_{10}{\Big(98+\sqrt{x^2-12x+36}\Big)}$ $\,=\,$ $2$

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