SOLUTION: Not understanding how to "SIMPLIFY" this; log9 1/729 (log nine, 1 over 729) My answer options are; 3, 81, -81, -3 I would like to see the steps to get the correct answer.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Not understanding how to "SIMPLIFY" this; log9 1/729 (log nine, 1 over 729) My answer options are; 3, 81, -81, -3 I would like to see the steps to get the correct answer.      Log On


   

Question 976823: Not understanding how to "SIMPLIFY" this; log9 1/729
(log nine, 1 over 729)
My answer options are; 3, 81, -81, -3
I would like to see the steps to get the correct answer.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
log%289%2C%281%2F729%29%29
=log%28%281%2F729%29%29%2Flog%28%289%29%29
=%28log%28%28+1%29%29-log%28%28729%29%29%29%2Flog%28%283%5E2%29%29.......since log%28%28+1%29%29=0, log%28%28729%29%29=log%283%5E6%29 and log%28%289%29%29=log%28%283%5E2%29%29, we have
=0-log%28%283%5E6%29%29%29%2Flog%28%283%5E2%29%29
=-6log%28%283%29%29%2F2log%28%283%29%29
=-6cross%28log%28%283%29%29%29%2F2cross%28log%28%283%29%29%29
=-6%2F2
=-3
so, your answer is -3

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Not understanding how to "SIMPLIFY" this; log9 1/729
(log nine, 1 over 729)
My answer options are; 3, 81, -81, -3
I would like to see the steps to get the correct answer.
log+%289%2C+%281%2F729%29%29

log+%289%2C+%289%5E-3%29%29 ------- Replacing 1%2F729 with 9%5E-3

9%5E%22%3F%22+=+9%5E-+3

highlight_green%28log%289%2C+%281%2F729%29%29+=+-+3%29