How do you solve the equation log(x)+log(x-8)=log9?

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Noah G Share
Feb 9, 2018

Answer:

#x= 9#

Explanation:

Use #log_a n + log_a m = log_a (nm)#.

#log(x(x - 8)) = log9#

Therefore:

#x^2 - 8x = 9#

#x^2 - 8x - 9 = 0#

#(x- 9)(x + 1) = 0#

#x = 9 or -1#

But #x= -1# is impossible because the logarithm function is undefined. If you test #x = 9# in the equation you will immediately see it works as #log(9) + log(9 - 8) = log(9) + log(1) = log(9) + 0 = log(9)#

Hopefully this helps!

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