SOLUTION: Please help us solve this log. prob my Maths teacher is also confused: log x = 1/3 log 8 + log 9 - 1/3 log 27 Thank you in advance.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help us solve this log. prob my Maths teacher is also confused: log x = 1/3 log 8 + log 9 - 1/3 log 27 Thank you in advance.      Log On


   

Question 505121: Please help us solve this log. prob my Maths teacher is also confused:
log x = 1/3 log 8 + log 9 - 1/3 log 27
Thank you in advance.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Logx+=+%281%2F3%29Log8%2BLog9-%281%2F3%29Log27 First, apply the "power rule" for logarithms:
n%2ALogM+=+LogM%5En
Logx+=+Log8%5E%281%2F3%29%2BLog9-Log27%5E%281%2F3%29 Substitute 8%5E%281%2F3%29+=+2 and 27%5E%281%2F3%29+=+3
Logx+=+Log2%2BLog9-Log3 Now apply the "product rule" for logarithms:
LogM%2BLogN+=+Log%28M%2AN%29
Logx+=+Log%282%2A9%29-Log3 Now apply the "quotient rule" for logarithms:
LogM-LogN+=+Log%28M%2FN%29
Logx+=+Log%2818%2F3%29
Logx+=+Log6 and if LogM+=+LogN then M+=+N so...
highlight%28x+=+6%29