# Graphing log Function

• Nov 30th 2009, 09:12 PM
hovermet
Graphing log Function
Graph
y=log base 3 (x+7)
It asks to graph, but i am just having problem solving for points(Y)

I know that you can also graph this function in exponential form
3^y=x+7

however, i tried to substitute in for x in the log function, but getting wrong answers
x=-7
y=log base 3(-7+7) = 1

expo
x=-6
3^y=-6+7
3^y=1
y=1

I am substituting different numbers for x but getting same answer, in fact the -6 is correct not the -7.

How do i find y in a using the log function?

Thank You
• Nov 30th 2009, 10:33 PM
earboth
Quote:

Originally Posted by hovermet
Graph
y=log base 3 (x+7)
It asks to graph, but i am just having problem solving for points(Y)

I know that you can also graph this function in exponential form
3^y=x+7

however, i tried to substitute in for x in the log function, but getting wrong answers
x=-7
y=log base 3(-7+7) = 1 <<<<<< log(0) is not defined!

...

If you don't want to use a calculator you should get powers of 3 as argument of the log function:

$y = \log_3(x-7)$
Therefore:

$y = \log_3(8-7)~\implies~y = 0$
$y = \log_3(10-7)~\implies~y = 1$
$y = \log_3(16-7)~\implies~y = 2$
$y = \log_3\left(\frac{22}3-7\right)~\implies~y = -1$

If you are allowed to use a calculator use the base-change-formula to get the y-values for any x > 7:

$y = \log_3(x)~\implies~y=\dfrac{\ln(x)}{\ln(3)}$