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### Section 6-3 : Solving Exponential Equations

4. Solve the following equation.

${7^{4 - x}} = {7^{4x}}$

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Start Solution

Recall the property that says if $${b^x} = {b^y}$$ then $$x = y$$. Since each exponential has the same base, 7 in this case, we can use this property to just set the exponents equal. Doing this gives,

$4 - x = 4x$ Show Step 2

Now 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*}4 - x & = 4x\\ 4 & = 5x\hspace{0.25in} \to \hspace{0.25in}x = \frac{4}{5}\end{align*}

So, the solution to the equation is then : $$\require{bbox} \bbox[2pt,border:1px solid black]{{x = \frac{4}{5}}}$$.