Question

Solve this exponential equation:
2^x-5 = 64^ 3x+1

Answer 1

confused about the 64^3x+1 is it supposed to be that or 64^3?

Answer 2

\[
\\2^{x-5} = 64^{3x + 1}
\\2^{x-5} = 2^{6^{3x + 1}}
\\2^{x-5} = 2^{6(3x + 1)}
\\ x - 5 = 6(3x + 1)
\\x - 5 = 18x + 6
\\-5 - 6 = 18x - x
\\-11 = 17x
\\-\frac{11}{17} = x
\]