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Solving Exponential Equations

Solving Exponential Equations 1.8 - Solution

arrow_back Return to Solving Exponential Equations
We have been given two equivalent expressions with the same base. Since both sides of the exponential equation are equal, the exponents must also be equal. 73x+5=71x3x+5=1x\begin{gathered} 7^{3x+5} = 7^{1-x} \quad \Leftrightarrow \quad 3x+5=1-x \end{gathered} We can now solve the above equation.
3x+5=1x3x+5=1-x
4x+5=14x+5=1
4x=-44x=\text{-}4
x=-1x=\text{-}1