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#