Question 1241: Solve 5^3x= 3^(x+4) for x.
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! Apply log (base 10) on both sides, we have
log 5^3x = log 3^(x+4),
Use log a^b = b log a, we have
Or 3x log 5 = (x+4) log 3,
Remove x log 3 to the left hand side and factor out x:
(3 log 5 - log 3)x = 4 log 3,
Or (log 5^3 - log 3)x = 4 log 3,
Or (log 125 - log 3)x = 4 log 3,
Or (log 125/3)x = 4 log 3,
So, x = 4 log 3/log (125/3)
If we convert it to log of base 3,we have
x = 4 log3 3/log3 (125/3)
= 4 / (log3 125 -1)
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