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Section 6.3 : Solving Exponential Equations
1. Solve the following equation.
\[{6^{2x}} = {6^{1 - 3x}}\]Show All Steps Hide All Steps
Start SolutionRecall the property that says if \({b^x} = {b^y}\) then \(x = y\). Since each exponential has the same base, 6 in this case, we can use this property to just set the exponents equal. Doing this gives,
\[2x = 1 - 3x\] Show Step 2Now all we need to do is solve the equation from Step 1 and that is a simple linear equation. Here is the solution work.
\[\begin{align*}2x & = 1 - 3x\\ 5x & = 1\hspace{0.25in} \to \hspace{0.25in}x = \frac{1}{5}\end{align*}\]So, the solution to the equation is then : \(\require{bbox} \bbox[2pt,border:1px solid black]{{x = \frac{1}{5}}}\).