How do you evaluate $log_9 729$ ?

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Answer 1 · 2016-08-07T13:35:09

When I write $log_(a)b=c$ . I state explicitly that $a^c=b$

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 $log_(9)729$ $=$ $3$ .

Answer 2 · 2016-08-07T18:42:48

$3$

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+

$x = (log729)/(log9) = 3$

It really is easier to just learn them!

How do you evaluate log_9 729log_9 729?