SOLUTION: 8^(x+3)=9^x x=52.965 but please explain how to get there.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 8^(x+3)=9^x x=52.965 but please explain how to get there.      Log On


   

Question 1000716: 8^(x+3)=9^x
x=52.965 but please explain how to get there.
Found 2 solutions by fractalier, MathLover1:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
From 8^(x+3)=9^x, apply laws of logs to get
log(8^(x+3))=log(9^x)
and
(x+3)log8 = xlog9
xlog8 + 3 log 8 = x log 9
Collect like terms and solve for x...
xlog8-xlog9 = - 3log8
x(log8-log9)=-3log8
x = -3log8 / (log8-log9)
Now plug in values
x = -3(.903)/(.903-.954)
x = 52.965

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

8%5E%28x%2B3%29=9%5Ex
%282%5E3%29%5E%28x%2B3%29=%283%5E2%29%5Ex
2%5E%283x%2B9%29=3%5E%282x%29
log%282%5E%283x%2B9%29%29=log%283%5E%282x%29%29
%283x%2B9%29log%282%29=%282x%29log%283%29...........since log%282%29=0.301029995663981and log%283%29=0.47712125471, we have
%283x%2B9%290.301029995663981=%282x%290.47712125471
0.903089986991943x%2B2.709269960975829=0.95424250942x
2.709269960975829=0.95424250942x-0.903089986991943x
2.709269960975829=0.05115252243x
x=2.709269960975829%2F0.05115252243
x+=+52.9645
or, rounded to three decimals
x=52.965