SOLUTION: How do I change this to a quotient or product? {{{ log(4,(x+3)) + log(4,(x-3)) }}}

Question 408784: How do I change this to a quotient or product?

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

I think you have been asked to rewrite your expression as the log of a product or quotient. If so, there are a couple of properties fo logarithms for this:

As you can see, the first property applies if there is a "+" between the two logarithms and the second one applies if there is a "-".

These properties require

Two logarithms of the same base.
Two logarithms with coefficients of 1.

Your logarithms meet both requirements. Your logarithms have a "+" between them so the first property applies. So:

RELATED QUESTIONS
How do i write these as a single logarithm? 1) (log 3 - log 4) - log 2 2) log 2 +... (answered by Boreal)

Solve both algebraically and graphically. 4^(3x-1)=90 log(4^3x-1)=log(90)... (answered by Earlsdon)

Hi. I need some help with a math problem. log[x] (x+4) + log[3] (x-2) = 3 I have no... (answered by richard1234)

Solve for x to the nearest hundredth 2^x = 3/16 2^(x+4) = 3 x+4 = {{{ log( 2, 3 )... (answered by josgarithmetic)

Hi, this is my second time asking a question....both were on logarithms :( Solve for... (answered by Alan3354,MathTherapy)

how do you solve this 2 log (x + 4 ) -log (x+2 ) = 3 + log (x - 2 ) 10 (answered by stanbon,Alan3354)

how do i solve (log base 4 (x+3))+(log base 4... (answered by stanbon,solver91311)

How do I condense this expression to a single logarithm? {{{ log z+log x / 3 + log y /... (answered by lwsshak3)

How do I solve log base 4(x+5)=3+log base... (answered by stanbon,MathTherapy)