How do you solve $2^(5x)/4^(3x)=8*16^(9x)$ ?

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Answer 1 · 2017-04-16T12:17:36

$x=-3/37$

Given:

$2^(5x)/4^(3x)=8*16^(9x)$

This can be rewritten in terms of powers of $2$ ...

$2^(5x)/((2^2)^(3x)) = 2^3*(2^4)^(9x)$

Then using:

$(a^b)^c = a^(bc)" "$ (when $a > 0$ )

we can rewrite this as:

$2^(-x) = 2^(5x-6x) = 2^(5x)/2^(6x) = 2^3*2^(36x) = 2^(36x+3)$

Note that $2^x$ is a one-one function as a real function, so the exponents are equal for the real solution and we find:

$-x = 36x+3$

Hence:

$x = -3/37$

How do you solve 2^(5x)/4^(3x)=8*16^(9x)2^(5x)/4^(3x)=8*16^(9x) ?