How do you solve #4^(3x)=3^(x-4)#?

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Answer 1 · 2015-12-01T01:24:20

#x = -(4ln(3))/(3ln(4) - ln(3))#

For this problem, we will be using the property of logarithms that

#ln(a^x) = xln(a)#

#4^(3x) = 3^(x-4)#

#=> ln(4^(3x)) = ln(3^(x-4))#

#=> 3xln(4) = (x-4)ln(3)

#=> 3xln(4) - xln(3) = -4ln(3)#

#=> x(3ln(4) - ln(3)) = -4ln(3)#

#=> x = -(4ln(3))/(3ln(4) - ln(3))#