1. ## working with logarithms?

so my advanced functions teacher didn't really explain this lesson well and i can't seem to figure it out on my own.

if you could be kind enough to explain the process i would greatly appreciate it!

2. The logarithm of a number y with respect to a base b is the exponent to which we have to raise b to obtain y.

the definition would be:

$\displaystyle x = log_{b} y \Longleftrightarrow b^x = y$

and we say that x is the logarithm of y with base b if and only if b to the power x equals y.

For example:

$\displaystyle 10^2 = 100 \Longleftrightarrow log_{10} 100 = 2$

and, $\displaystyle 10^{-2} = 0.01 \Longleftrightarrow log_{10} 0.01 = -2$

Based on this, can you now complete your question?!

3. Originally Posted by yolanda
so my advanced functions teacher didn't really explain this lesson well and i can't seem to figure it out on my own.

if you could be kind enough to explain the process i would greatly appreciate it!
$\displaystyle \displaystyle\ \log_9\left(\frac{1}{3}\right)=x$

$\displaystyle \displaystyle\ \log_3\left(\frac{1}{9}\right)=y$

Imagine a "fog" surrounding the "log" and the base slides over to the other side,
so we get

$\displaystyle \displaystyle\frac{1}{3}=9^x$

$\displaystyle \displaystyle\frac{1}{9}=3^y$

Now x and y will be easier to derive.

4. thank you