Question

Part 1: Find the solution to the equation 64^(3 + x) = 4^(2x)?
Please explain!!

Answer 1

\[64^{(3 +x)}=4^{2x}\]

Answer 2

We'll get the same, and we know that 64 can be expressed as 4 cubed.
\(\Large \color{purple}{\rightarrow (4^3)^{3 + x} = 4^{2x} }\)

Multiply the exponents
\(\Large \color{purple}{\rightarrow 4^{9 + 3x} = 4^{2x} }\)

We can make a normal equation
\(\Large \color{purple}{\rightarrow 9 + 3x = 2x }\)

\(\Large \color{purple}{\rightarrow 9 = -x }\)

\(\Large \color{purple}{\rightarrow x = -9 }\)