Answer
$x=-5$
Work Step by Step
The given equation is
$\Rightarrow 7^{x-5}=49^{x}$
Rewrite $49$ as $7^2$.
$\Rightarrow 7^{x-5}=(7^2)^{x}$
Use $(a^n)^m=a^{n\cdot m}$
$\Rightarrow 7^{x-5}=7^{2x}$
Equate the exponents.
$\Rightarrow x-5=2x$
Subtract $x$ from each side.
$\Rightarrow x-5-x=2x-x$
Simplify.
$\Rightarrow -5=x$
Check: $(x=-5)$
$\Rightarrow 7^{-5-5}=49^{-5}$
$\Rightarrow 7^{-10}=\frac{1}{49^{5}}$
$\Rightarrow \frac{1}{7^{10}}=\frac{1}{49^{5}}$
$\Rightarrow \frac{1}{282475249}=\frac{1}{282475249}$
True.
Hence, the solution is $x=-5$.
