Convert to Logarithmic Form 4(8^x)=64

$4 (8^{x}) = 64$

Simplify both sides of the equation.

Rewrite $4$ as $2^{2}$ .

$2^{2} \cdot 8^{x} = 64$

Rewrite $8$ as $2^{3}$ .

$2^{2} \cdot {(2^{3})}^{x} = 64$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2^{2} \cdot 2^{3 x} = 64$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{2 + 3 x} = 64$

Convert the exponential equation to a logarithmic equation using the logarithm base $(2)$ of the right side $(64)$ equals the exponent $(2 + 3 x)$ .

$\log_{2} (64) = 2 + 3 x$