How do you solve #7^( x + 4) = 243^( x + 6)#?

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Answer 1 · 2017-11-22T11:59:21

#x approx -7.0972#

#7^(x+4) = 243^(x+6)#

First notice: #243 = 3^5#

Hence, #7^(x+4) = 3^(5(x+6))#

Since #3 and 7# are prime we cannot simplify this further.

#->(x+4)ln7 = 5(x+6)ln3#

#(x+4)/(5(x+6)) = ln3/ln7 approx 1.09861/1.94591#

#(x+4)/(5(x+6)) approx 0.564575#

#x+4 approx 2.82287x+16.93725#

#1.82287x = -12.93725#

#x approx -7.0972#