Question

4^-2x * 4^x = 64
solve for x

Answer 1

\[4^{-2x}*4^{x}=64\]

Since the bases are the same just add the exponents.

\[4^{-x}=64\]

To solve for an exponent use logarithms

\[\log_{10}4^{-x}=\log_{10}64 \]\[-x \log_{10}4=\log_{10}64 \]\[-x=\log_{10}64/\log_{10}4 \]