# Math Help - Logarithm simplification

1. ## Logarithm simplification

I am having trouble solving this log.

Simply:

25^ log5(xy) + log ( xg * (root)y over (root) x)

My simplification is:

(xy)^2 + log (x^3/4 y^1/2 g /1)

2. Do you mean

A: $25^{\log_5(xy) + log_{10} \left(xg \sqrt{\dfrac{y}{x}\right)$

B: $25^{\log_5(xy)} + \log_{10}\left(xg \sqrt{\dfrac{y}{x}\right)$

C: Something entirely different

3. Part B: but the x in the second log is also square rooted (in the denominator)

4. so how would this be simplified?
I can simplify the first part, but am having trouble with the second.

5. ## ...

so how would this be simplified?
I can simplify the first part, but am having trouble with the second.

6. So, you need to simplify:

$\displaystyle 25^{\log_5(xy)} + \log\left(xg \sqrt{\dfrac{y}{\sqrt{x}}\right)\ ?$

You may want to split up the logarithm to the sum of logarithms, depending upon what's meant by 'simplify'.

7. Yes
so would the second portion be:
log(xg) + log(y^1/2) - log(x^1/4)
log(x)+log(g)+log(y^1/2)-log(x^1/4)

8. Originally Posted by FallenStar117
Yes
so would the second portion be:
log(xg) + log(y^1/2) - log(x^1/4)
log(x)+log(g)+log(y^1/2)-log(x^1/4)
You could also take the "1/2" and "1/4" out of the logarithms.