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log10(x+2)+log10x-1 log10(3/2)

Customer Question

log10(x+2)+log10x-1=log10(3/2)
Submitted: 6 years ago.
Category: Math Homework
Expert:  abozer replied 6 years ago.

abozer :

Hi,

abozer :

We can start solving this question by bringing all terms to the same base. 10 in this case.

abozer :

Let's use the identity log10(10) = 1

abozer :

Substitute log10(10) instead of 1 on the left hand side,

abozer :

log10(x+2) + log10x - log10(10) = log10(3/2)

abozer :

now, combine the terms on the left hand side,

abozer :

log10( (x+2)x/10 ) = log10(3/2)

abozer :

reduces to,

abozer :

(x + 2)x/10 = 3/2

abozer :

multiply both sides by 10,

abozer :

(x + 2)x = 15

abozer :

rearrange,

abozer :

x^2 + 2x - 15 = 0

abozer :

factor,

abozer :

(x + 5)(x - 3) = 0

abozer :

x = 5

abozer :

sorry

abozer :

x = -5 and x = 3

abozer :

Let me know if you have any questions.