SOLUTION: Solve: 5^(x+2)=3^(x) I understand that its supposed to be in log form, but I don't know what do once I get it there. Thanks so much!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve: 5^(x+2)=3^(x) I understand that its supposed to be in log form, but I don't know what do once I get it there. Thanks so much!      Log On


   

Question 873015: Solve:
5^(x+2)=3^(x)
I understand that its supposed to be in log form, but I don't know what do once I get it there. Thanks so much!
Found 3 solutions by josgarithmetic, Edwin McCravy, MathTherapy:
Answer by josgarithmetic(39632) About Me  (Show Source):
You can put this solution on YOUR website!
log%2810%2C5%5E%28x%2B2%29%29=log%2810%2C3%5Ex%29
%28x%2B2%29log%2810%2C5%29=x%2Alog%2810%2C3%29
x%2Alog%2810%2C5%29%2B2%2Alog%2810%2C5%29=x%2Alog%2810%2C3%29
2%2Alog%2810%2C5%29=x%2Alog%2810%2C3%29-x%2Alog%2810%2C5%29
x%28log%2810%2C%283%2F5%29%29%29=2%2Alog%2810%2C5%29
highlight%28x=%282%2Alog%2810%2C5%29%29%2F%28log%2810%2C%283%2F5%29%29%29%29
still a few more steps, that mostly just needs to be computed.

Answer by Edwin McCravy(20067) About Me  (Show Source):
You can put this solution on YOUR website!
You might find it easier to use substitution of
a logarithm by a letter to keep from getting
bogged down in the notation.

5%5E%28x%2B2%29%22%22=%22%223%5E%28x%29

Take logs of both sides

log%28%285%5E%28x%2B2%29%29%29%22%22=%22%22log%28%283%5E%28x%29%29%29

Use this rule:

"The logarithm of an exponential number is the 
exponent times the logarithm of the base."

(x+2)log(5) = x*log(3)

Now substitute the letter A for log(5) and B for  log(3)

(x+2)A = xB

A(x+2) = Bx

Ax+2A = Bx

Ax-Bx = -2A

x(A-B) = -2A

x = -2A%2F%28A-B%29

Now replace the letter A by log(5) 
and the letters B by log(3) 

x = -2log%28%285%29%29%2F%28log%285%29-log%283%29%29

Then take a calculator and find x = -6.301320206

Edwin

Answer by MathTherapy(10559) About Me  (Show Source):
You can put this solution on YOUR website!

Solve:
5^(x+2)=3^(x)
I understand that its supposed to be in log form, but I don't know what do once I get it there. Thanks so much!


highlight_green%28x+=+-+6.30132%29 

You can do the check!! 



If you need a complete and detailed solution, let me know!!



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