Answer
$x=-\dfrac{1}{2}$
Work Step by Step
Expressing both sides of the given equation, $
7^{2x+3}=49
,$ with the same base gives:
\begin{align*}
7^{2x+3}&=7^2
.\end{align*}
Since the bases in the equation above are the same, the exponents can be equated. That is,
\begin{align*}\require{cancel}
2x+3&=2
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
2x+3-3&=2-3
\\
2x&=-1
\\\\
\dfrac{\cancel2x}{\cancel2}&=-\dfrac{1}{2}
\\\\
x&=-\dfrac{1}{2}
.\end{align*}
Hence, the solution to the equation $7^{2x+3}=49$ is $x=-\dfrac{1}{2}$.
