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

1 Answer
Apr 16, 2017

x=-3/37

Explanation:

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