Question

Solve the equationTexFormula1" title="16 {}^{2x - 3} = 8 {}^{4x} " alt="16 {}^{2x - 3} = 8 {}^{4x} " align="absmiddle" class="latex-formula">
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Answer 1

Answer:

n = -3

Step-by-step explanation:

$16=2^4\\\\8=2^3\\\\16^{2n-3}=8^{4n}\\\\(2^4)^{2n-3}=(2^3)^{4n}\qquad\txt{use}\ (a^n)^m=a^{nm}\\\\2^{(4)(2n-3)}=2^{(3)(4n)}\iff4(2n-3)=12n\qquad\text{use the distributive property}\\\\(4)(2n)+(4)(-3)=12n\\\\8n-12=12n\qquad\text{subtract}\ 8n\ \text{from both sides}\\\\-12=4n\qquad\text{divide both sides by 4}\\\\\dfrac{-12}{4}=\dfrac{4n}{4}\\\\-3=n\to n=-3$