How do you solve #3^(x+4)=2^(1-3x)#?

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Answer 1 · 2018-08-03T07:59:20

The solution is #x=-1.165#

Solve by taking the logs on both sides of the equation

#3^(x+4)=2^(1-3x)#

#ln(3^(x+4))=ln(2^(1-3x))#

#(x+4)ln3=(1-3x)ln2#

#xln3+4ln3=ln2-3xln2#

#xln3+3xln2=ln2-4ln3#

#x(ln3+3ln2)=ln2-4ln3#

#x=(ln2-4ln3)/(ln3+3ln2)#

#x=-3.701/3.178=-1.165#