how do i solve this? logarithm question

Question

anonymous · Answer

not sure where to begin.

anonymous · Answer

Take Log on both the sides...

anonymous · Answer

Log to the base of 10 of course..
Then you need to use Power rule of Logarithms ie:
$\log(a)^n = n \cdot log(a)$

anonymous · Answer

log 3x=10^12?

anonymous · Answer

or no, 3 log x=10^12

anonymous · Answer

How you got 10^12?? You are supposed to take Logs on both sides, do not take Log on one side and AntiLog on other side..

anonymous · Answer

How you got x in logs and 3 outside of Logs??

anonymous · Answer

oh, i thought there was automatically a base of 10 and then you just take that number and make it the exponent. im not sure what type of equation im thinking of.

anonymous · Answer

i cant remember how to take the log of the equation, sorry. ive done lots of math these past few days and everything is getting jumbled up in my head.

anonymous · Answer

$3^x = 12$
$\log(3^x) = \log(12)$
$x \cdot \log(3) = \log(12)$

anonymous · Answer

Now find $x$ by dividing both the sides by $\log(3)$.. Base is 10, so while calculating, don't forget to take base as 10..

anonymous · Answer

ah okay. do i plug in log(12)/log(3) to my calculator?

anonymous · Answer

where does the base of 10 come in then?

anonymous · Answer

Yes for sure..!!

anonymous · Answer

okay i got 2.2618. now what were you saying about the base of 10 though?

anonymous · Answer

or is that my final answer^?

anonymous · Answer

What is the value of log(3) you calculated?

anonymous · Answer

.4771

anonymous · Answer

Yeah you are right... :) Good..

anonymous · Answer

$\dagger$

anonymous · Answer

so what is my final answer then?

anonymous · Answer

what are the steps for answering a problem like this? you take the log, then divide the logs and is that your answer?

anonymous · Answer

Yes it is..

anonymous · Answer

okay was just making sure, cause you asked about log(3) after i had given that answer lol