SOLUTION: Hi, my problem is: Solve the equation log3(1/27) =X

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Question 136356This question is from textbook College Algebra
: Hi, my problem is: Solve the equation log3(1/27) =X This question is from textbook College Algebra

Found 2 solutions by Edwin McCravy, vleith:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, my problem is: Solve the equation log%283%2C%281%2F27%29%29+=X 


Learn this principle of logarithms:

The logarithm equation log%28B%2C%28A%29%29=C is always equivalent to
the exponential equation B%5EC=A

So your logarithm equation

log%283%2C%281%2F27%29%29=x 

is equivalent to the exponential equation 

3%5Ex=1%2F27.

Now write 27 as 3%5E3

3%5Ex=1%2F3%5E3

Now write 1%2F3%5E3 as 3%5E%28-3%29

3%5Ex=3%5E%28-3%29

Now use the principle:

If B%3E0 and B%3C%3E1, then if B%5EA=B%5EC then A=C

So since 3%5Ex=3%5E%28-3%29, and 3%3E0 and 3%3C%3E1, then

x+=+-3

Edwin

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Given: log3%281%2F27%29+=X
3%5E%28log3%281%2F27%29%29+=3%5EX
1%2F27+=+3%5Ex+
3%5E%28-3%29+=+3%5Ex+
x = -3
Or another way
log3%281%2F27%29+=X
Log%281%2F27%29+%2F+Log%283%29+=+x+
-3 = x