Solve the logarithmic equation for x. log18(x − 5) + log18(x + 2) = 1 x =

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Solve the logarithmic equation for x.
log18(x − 5) + log18(x + 2) = 1

x = 

Jul 16th, 2015

Hi !

log18(x - 5) + log18(x + 2) = 1

With same bases we can write

log18[(x - 5)(x + 2)] = 1

Now we can write

log18[(x - 5)(x + 2)] = log18(18^1)

So

(x - 5)(x + 2) = 18^1

x^2 + 2x - 5x - 10 = 18

x^2 - 3x - 10 = 18

x^2 - 3x - 10 - 18 = 0

x^2 - 3x - 28 = 0

x^2 + 4x - 7x - 28 = 0

x(x + 4) - 7(x + 4) = 0

(x + 4)(x - 7) = 0

x = - 4    x = 7

Hence 

Hope you get it. Thanks :)
Jul 16th, 2015

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