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

Printable View

- May 25th 2011, 12:16 PMhomeylova223Logarithmic functions?
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 - May 25th 2011, 12:23 PMTheEmptySet
- May 25th 2011, 12:28 PMhomeylova223
I mean the former the one where both x and negative one are in the parenthesis.

- May 25th 2011, 12:38 PMTheEmptySet
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? - May 25th 2011, 01:36 PMhomeylova223
For my second question

y=2 log 2 x Would I do this

2^y=2x Then would I just divide by 2? - May 25th 2011, 03:08 PMskeeter