SOLUTION: Log 729 base 3 is equal to x

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Question 999850: Log 729 base 3 is equal to x
Found 3 solutions by josgarithmetic, mananth, Theo:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
log%283%2C729%29=x

log%283%2C%2881%2A9%29%29=x

log%283%2C%283%5E4%2A3%5E2%29%29=x

log%283%2C%283%5E6%29%29=x
You can finish this and should be able to SEE the answer.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
log[3]729=x

log[3](3^6)=x
3%5Ex+=+3%5E6
x=6

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
couple of ways to solve it.

one way:

convert from log form to exponent form and then solve and then convert back to log form.

log3(729) = x if and only if 3^x = 729

through iteration it was determined that x = 6

you get 3^6 = 729

this is true if and only if log3(729) = 6

you get x = 6.

it won't always be that easy because the exponent is not always an integer, so the better way is through the use of a calculator and the log base conversion formula.

log3(729) = x

convert log base to 10 or e because those are the log bases that your calculator can handle.

log base 10 is the log function key on your calculator.

log base e is the ln function key on your calculator.

the conversion formula for log base 10 is:

log3(729) = log(729)/log(3)

the conversion formuls for log base e is:

log3(729) = ln(729)/ln(3)

both will get you the correct answer.

log(729)/log(3) = 6

ln(729)/ln(3) = 6