Graph each equation or inequality
1.y= log 5(x-1) This is what I did
y+1= log 5 x
5^y+1=x Would this be right of setting up the graph so that if y=0 x=5?
2. y=2 log 2 x I am slightly confused on how to start this
First you can graph in the method that you started above but you don't have to.
$\displaystyle y=\log_{5}(x-1) \iff 5^y=x-1 \iff x=5^y+1$
You can then pick y values to make a table. Note that the x values get large really quickly.
Or you can make the table directly from the function. First we know that the log of zero is undefined so when
$\displaystyle x-1=0 \iff x=1$
so there is a vertical asymptote when x=1.
Also you should know that
$\displaystyle \log_{a}(1)=0$
for any
$\displaystyle a > 0, \quad a \ne 1$
Now we can just pick powers of the bases to get
$\displaystyle \log_{5}\left(5^{n} \right)=n$
can you finish from here?