Algebra and Applications Test 2

$7^{\mathit{x}-1}+{11}^{\mathit{x}-1}=170$
Let the value of x = 3
So, $7^{3-1}+{11}^{3-1}=170$
$7^2+{11}^2=170$
$49+121=170$
$170=170$
Hence, x = 3 satisfies the given conditions.
If the value of x is greater or less than 3, then R.H.S is not equal to 170.
Hence, only one solution of the given equation exists.