Question 664119: Im having trouble solving Log base 3 of 27^-1 = x. i know to move the -1 in front of log and make it -1(log base 3 of 27)=x, but now im stuck. Can someone please help?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! log3(27^-1) = x
one way to solve this is shown below:
log3(27^-1) = x if and only if 3^x = 27^-1
take the log10 of both sides of this equation to get:
log10(3^x) = log10(27^-1)
since log10 is the LOG function of your calculator, this equation becomes:
LOG(3^x) = LOG(27^-1)
since,in general, log(a^b) = b*log(a), then this equation becomes:
x*LOG(3) = -1*LOG(27)
divide both sides of this equation to get:
x = -1*LOG(27)/LOG(3)
solve for x using your calculator to get:
x = -3
that's your answer.,
confirm by replacing x in your original equation with -3
you get:
log3(27^-1) = -3
you can convert log3 to log10 by using the log base conversion formula.
that formula is:
log3(27^-1) = log10(27^-1)/log10(3)
since log10 is equal to the LOG function of your calculator, this becomes:
log3(27^-1) = LOG(27^-1)/LOG(3)
use your calculator to solve this to get:
log3(27^-1) = -3
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