# Thread: logarithm help

1. ## logarithm help

1.express in terms of log a, log b.

$\log \frac{1}{ab^4}$

2.express as a single logarithm.

$\frac{1}{2}\log 80 - \frac{1}{2}\log 5$

thanks

2. Originally Posted by llkkjj24
1.express in terms of log a, log b.

$\log \frac{1}{ab^4}$

2.express as a single logarithm.

$\frac{1}{2}\log 80 - \frac{1}{2}\log 5$

thanks
Use these two facts:

$log(x\cdot y) = log(x) + log(y)$

$log(\frac{x}{y}) = log(x) - log(y)$

And for the second, note that $\frac{1}{2}log(80) - \frac{1}{2}log(5) = \frac{1}{2}(log(80)-log(5))$.

Can you do it now?

3. ye, i did it before, but my answer didn't match of the book.
so was hoping for someone to work it out so i can see my mistakes

4. Originally Posted by llkkjj24
so was hoping for someone to work it out so i can see my mistakes
Post your work so we can see your mistakes, it will be easier to assist you this way.

5. for 1 i had trouble of how to manipulate the fraction $\frac{1}{ab^4}$.
is this the correct form? $\log a - \log b ^ -4$

for 2 i did using the laws of logs.

$\log 80^\frac{1}{2} - \log 5^\frac{1}{2}$

then $\log \frac{\log \sqrt{80}}{\log \sqrt{5}}$

6. Using the properties posted above by Defunkt, you get:

$log\left ( \frac{1}{ab^4}\right )$

$\Rightarrow log(1)-\left[log(a)+log(b^4)\right]$

$\Rightarrow 0-log(a)-4log(b)$

$\Rightarrow -log(a)-4log(b)$

and for the second one:

$\frac{1}{2}log(80)-\frac{1}{2}log(5)$

$\Rightarrow \frac{1}{2}\left[log(80)-log(5)\right]$

$\Rightarrow\frac{1}{2}log(\frac{80}{5})$

$\Rightarrow\frac{1}{2}log(16)$

$\Rightarrow\log(16^\frac{1}{2})$

$\Rightarrow\log(4)$

7. Originally Posted by llkkjj24
for 1 i had trouble of how to manipulate the fraction $\frac{1}{ab^4}$.
is this the correct form? $\log a - \log b ^ -4$

for 2 i did using the laws of logs.

$\log 80^\frac{1}{2} - \log 5^\frac{1}{2}$

then $\log \frac{\log \sqrt{80}}{\log \sqrt{5}}$
You can also solve the second problem this way:

$\frac{1}{2}log(80)-\frac{1}{2}log(5)$

$\Rightarrow log\left ( \frac{\sqrt{80}}{\sqrt{5}}\right )$

$\Rightarrow log(4)$

(after rationalising and simplifying the fraction)

8. thanks , problem solved