SOLUTION: I am trying to help my niece with an equation. Solving with logarithms, the equation is 5^x=4^(x+3). I cannot remember for the life of me how to solve this..Can you help?

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Question 549482: I am trying to help my niece with an equation. Solving with logarithms, the equation is 5^x=4^(x+3). I cannot remember for the life of me how to solve this..Can you help?
Found 2 solutions by mananth, lwsshak3:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
5^x=4^(x+3)
x log 5=(x+3)log 4
xlog5-xlog4=3log4
x(log5-log4)=3lo4
x=3log4/(log5-log4)
use a calculator

Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
I am trying to help my niece with an equation. Solving with logarithms, the equation is 5^x=4^(x+3). I cannot remember for the life of me how to solve this.
**
using the exponent rule for logs:
xlog5=(x+3)log4
x/(x+3)=log4/log5
using calculator
x/(x+3)≈.8614
x=.8614x+3*.8614
x-.8614x=2.5841
.1386x=2.5814
x=2.5814/.1386=18.6185
Check:
5^x=5^18.6185=1.0322*10^13
4^(x+3)=4^(21.6185)=1.0366*10^13
difference due to rounding errors