Question

algebra: concepts and connections - plc solving exponential equations by rewriting the base which equation is equivalent to $2^{4x}=8^{x - 3}$? $2^{4x}=2^{2x - 6}$ $2^{4x}=2^{3x - 3}$ $2^{4x}=2^{2x - 3}$ $2^{4x}=2^{3x - 9}$

Explanation:

Step1: Rewrite 8 as base 2

$8 = 2^3$

Step2: Substitute into right-hand side

$8^{x-3} = (2^3)^{x-3}$

Step3: Apply exponent power rule

$(2^3)^{x-3} = 2^{3(x-3)} = 2^{3x-9}$

Step4: Equate with left-hand side

$2^{4x} = 2^{3x-9}$

Answer:

$\boldsymbol{2^{4x} = 2^{3x-9}}$