Methods for solving logarithmic equations

Methods

1) Exponentiate: $\log_a f(x)=\log_a g(x)\ \Rightarrow\ f(x)=g(x)$ when $f>0$ , $g>0$ , $a>0$ , $a\neq1$ . 2) Match bases or use the change-of-base formula (a separate advanced lesson — use when needed). 3) Substitute $t=\log_a x$ or $t=\lg x$ in expressions quadratic in a logarithm. 4) After solving, always plug into the domain: every $\log$ argument must be $>0$ .

Exponentiating can introduce extraneous roots if you forget $f,g>0$

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