SOLUTION: Hi please help me to solve 5^log x-4^log(x-1)=4^log x+5^log(x-1) Thanks and regards, AN

Question 486653: Hi
please help me to solve 5^log x-4^log(x-1)=4^log x+5^log(x-1)
Thanks and regards,
AN
Answer by chessace(471) (Show Source): You can put this solution on YOUR website!
Drop the "og "
5^Lx - 4^Lx-1 = 4^Lx + 5^Lx-1
Group sides:
5^Lx - 5^Lx-1 = 4^Lx + 4^Lx-1
Get all exponents to Lx-1:
5*5^Lx-1 - 5^Lx-1 = 4*4^Lx-1 + 4^Lx-1
Collect terms:
4*5^Lx-1 = 5*4^Lx-1
Un-cross multiply:
(5^Lx-1)/(4^Lx-1) = 5/4
Merge under common exponent:
(5/4)^Lx-1 = 5/4
Divide by 5/4:
(5/4)^Lx-2 = 1
X>0 and X^a = 1 --> a = 0:
Lx-2 = 0
Raise base (10 e.g.) to each side:
x-2 = 1
x = 3

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