How do you solve the exponential equation $8^{5 x} = 16^{3 x + 4}$ $8^(5x)=16^(3x+4)$ ?

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Answer 1 · 2017-03-08T00:22:11

$\Rightarrow x = \frac{16}{3}$ $implies x = 16/3$

$8^{5 x} = 16^{3 x + 4}$ $8^(5x)=16^(3x+4)$

$\Rightarrow {(2^{3})}^{5 x} = {(2^{4})}^{3 x + 4}$ $implies (2^3)^(5x)=(2^4)^(3x+4)$

$\Rightarrow 2^{15 x} = 2^{4 (3 x + 4)}$ $implies 2^(15x)=2^(4(3x+4))$

$\Rightarrow 15 x = 12 x + 16$ $implies 15x = 12x+16$

$\Rightarrow x = \frac{16}{3}$ $implies x = 16/3$

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