Algebra Examples

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

Step 1

Simplify both sides of the equation.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 2

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

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