Question

Evaluate each expression : Logs CLICK ! please.

Answer 1

\[\log _{9}9^{6}\]

Answer 2

The way to interpret this is,
"9 to what power gives us 9 to the sixth power?"

We start with a base of 9, `the base of our logarithm` and we got to \(\large 9^6\) somehow.

Answer 3

Another way to approach this is to apply some logarithm rules.
We can bring the exponent OUT of the logarithm and write it as a factor in front.\[\huge \log_9 9^{\color{royalblue}{6}} \qquad = \qquad \color{royalblue}{6}\log_9 9\]

Then from there, recognize that the base matches the argument (the thing inside of the log) which will always give us 1.\[\huge \color{royalblue}{6}\log_9 9 \qquad = \qquad \color{royalblue}{6}\cdot 1\]

Answer 4

and then ?

Answer 5

@zepdrix so i shouldnt do 9x9x9x9x9x9 and make it onto one big long number. leave it in exponent form ?

Answer 6

the answer's 1 then ?

Answer 7

@zepdrix

Answer 8

The answer is 6 :c see my second post? \(6\cdot1\)

Answer 9

okay , i saw that. thanks .