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

##### 1 Answer

Apr 16, 2017

#### Explanation:

Given:

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

This can be rewritten in terms of powers of

#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

#-x = 36x+3#

Hence:

#x = -3/37#