Expert: Sherry Wallin - 12/10/2008

Question
please help me find the sum/difference of log5[x2/y7] and log5 square root rs/9

Answer
Hi Krista~

     Hopefully we are communicating on what the problem is, this is what I think you meant:

log (base 5) of (x^2/y^7) plus/minus log (base 5) [sqrt of (rs/9)].

With that said, recall there are rules for sums and differences, in English this is that the sum of two logs is the product of the logs and the difference of two logs is the quotient of the logs.

For the Sum:

log (base 5) of (x^2/y^7)    log (base 5) [sqrt of (rs/9)]
= log(base 5){(x^2/y^7)[sqrt of (rs/9)]}

Remember if there is a power on the "argument" then the power comes out in front of the log as a factor so in this case sqrt means to the 1/2 power. This is kind of tricky because your whole argument needs to be to the 1/2 power, but all is not lost because you can square x^2 and y^7 and put them under the sqrt and bring it all to the 1/2 power:

this is what I mean: (x^2/y^7) = (x^4/y^14)^(1/2)
= log(base 5)[(x^4/y^14)(rs/9)]^(1/2)
=(1/2)log(base 5)(rsx^4/9y^14)

A similar trick would need to be done for the difference...

Math Prof