Systems of exponential and logarithmic equations

Approach

Common strategies: express $a^x$ or $\log_a x$ from one equation and substitute into the second; set $u=\lg x$ , $v=\lg y$ if sums of logs become a linear system after transforms; use $a^{\log_a b}=b$ to collapse exponential–logarithm pairs. After finding $(x,y)$ , check the domain of every $\log$ and $a^x>0$ .

Symmetric systems sometimes simplify with $t=x/y$ or the sum/difference of the unknowns

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