Question

7^\frac{x - 3}{8} = \sqrt{7}
the solution set is \\{\\ \\}.

Explanation:

Step1: Express both sides with base 7

We know that $\sqrt{7} = 7^{\frac{1}{2}}$. So the equation $7^{\frac{x - 3}{8}}=7^{\frac{1}{2}}$ holds.

Step2: Set exponents equal (since bases are same)

For exponential functions with the same base ($a^m=a^n\implies m = n$ when $a>0,a
eq1$), we set $\frac{x - 3}{8}=\frac{1}{2}$.

Step3: Solve for x

Multiply both sides by 8: $x - 3=\frac{1}{2}\times8 = 4$. Then add 3 to both sides: $x=4 + 3=7$.

Answer:

$\{7\}$