# maths

Solve
log(5x-1) = 2 + log(x-2)

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1. log(5x-1) = 2 + log(x-2)
log(5x-1) - log(x-2) = 2
log ( (5x-1)/(x-2) ) = 2
(5x-1)/(x-2) = 10^2 = 100

100x - 200 = 5x-1
95x = 199
x = 199/95

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posted by Reiny
2. How did you arrive at 10^2?

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2. 👎 0
posted by Lindsay
3. By the definition of logs

loga b = c <------> a^c = b

so if log10( (5x-1)/(x-2) ) = 2 , then
10^2 = ( (5x-1)/(x-2) )

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posted by Reiny

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