# Simplify log ad graph exponential

• May 16th 2009, 09:59 PM
nerdzor
Simplify $\displaystyle \log a^3 - \log a^2$

I'm not sure if this is right but is it either:

a) $\displaystyle = 3\log_{10} a - 2\log_{10} a$
$\displaystyle =\log_{10} a (3-2)$
$\displaystyle =\log_{10} a {1}$
$\displaystyle a=0$

OR

b) $\displaystyle \log a^3 - \log a^2$
$\displaystyle =\log_{10} \frac{a^3}{a^2}$
$\displaystyle =\log_{10} a$

???

To graph $\displaystyle y=e^x$
$\displaystyle -1 \leq x\leq 3$
Is it just the exact same as a normal $\displaystyle y=e^x$ but asymptotic at $\displaystyle x=-1$ and $\displaystyle x=3$?

How can I find the gradient of the tangent at (0,1)?
• May 16th 2009, 11:27 PM
Quote:

Originally Posted by nerdzor
Simplify $\displaystyle \log a^3 - \log a^2$

I'm not sure if this is right but is it either:

a) $\displaystyle = 3\log_{10} a - 2\log_{10} a$
$\displaystyle =\log_{10} a (3-2)$
$\displaystyle =\log_{10} a {1}$
$\displaystyle a=0$

OR

b) $\displaystyle \log a^3 - \log a^2$
$\displaystyle =\log_{10} \frac{a^3}{a^2}$
$\displaystyle =\log_{10} a$

b is right .
• May 16th 2009, 11:55 PM
Singaporean
b is right