# How do you evaluate log_9 729?

Aug 7, 2016

When I write ${\log}_{a} b = c$. I state explicitly that ${a}^{c} = b$

#### Explanation:

Typically we use sensible bases for logarithms such as $10$ or $e$.

But with your problem we have ${\log}_{9} 729$.

And thus if ${\log}_{9} 729 = x$, then ${9}^{x} = 729 = {9}^{3}$.

Clearly ${\log}_{9} 729$ $=$ $3$.

Aug 7, 2016

$3$

#### Explanation:

In log form, the question being asked is :

"To what power must 9 be raised to equal 729?"

It really is a huge advantage to know all the powers up to 1,000 by heart.

In this case you will recognize $729 = {9}^{3}$

Therefore ${\log}_{9} 729 = 3$

Without knowing this, you will have to do the whole log route...

${\log}_{9} 729 = x$
${9}^{x} = 729$

#xlog9 = log729+

$x = \frac{\log 729}{\log 9} = 3$

It really is easier to just learn them!