Use the Laws of Logarithms to combine the expression

Algebra
Tutor: None Selected Time limit: 1 Day

Use the Laws of Logarithms to combine the expression.

log7(x2 − 36) − log7(x − 6)
 
Apr 13th, 2015

Since the logs have the same base (7), the subtration outside can be turned into division inside.

log [base7] {(x^2-36)/(x-6)} now we just use algebra.

We can factor out x^2-36 to (x+6)(x-6) *the form is difference of squares. Now we have this:

(x+6)(x-6) / (x-6) in the log parenthesis. This can be simplified by canceling out the x-6 to give us x+6.

Answer : log [base7] (x+6)

*The rule I used is this

log[b] (x) - log[b] (y) = log[b] (x/y) 

conversely, we multiply in the presence of addition

log[b] (x) + log[b] (y) = log[b] (xy)

Apr 13th, 2015

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