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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
