SOLUTION: Use the properties of lagarithms eo expand: log[7]7x^2y^3/z. Need some help on this one. Thanks.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Use the properties of lagarithms eo expand: log[7]7x^2y^3/z. Need some help on this one. Thanks.      Log On


   

Question 598803: Use the properties of lagarithms eo expand: log[7]7x^2y^3/z.
Need some help on this one. Thanks.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Expand:
Log%5B7%5D%287x%5E2y%5E3%2Fz%29 First, apply the "quotient rule" for logarithms: Log%5Bb%5D%28M%2FN%29+=+Log%5Bb%5D%28M%29-Log%5Bb%5D%28N%29 to get:
Log%5B7%5D%287x%5E2y%5E3%29-Log%5B7%5D%28z%29 Next, apply the "product rule" for logarithms: Log%5Bb%5D%28M%2AN%29+=+Log%5Bb%5D%28M%29%2BLog%5Bb%5D%28N%29 to get:
Log%5B7%5D%287%29%2BLog%5B7%5D%28x%5E2%29%2BLog%5B7%5D%28y%5E3%29-Log%5B7%5D%28z%29 Now apply the "power rule" for logarithms: Log%5Bb%5D%28M%5En%29+=+nLog%5Bb%5D%28M%29 to get:
Log%5B7%5D%287%29%2B+2Log%5B7%5D%28x%29%2B3Log%5B7%5D%28y%29-Log%5B7%5D%28z%29 Finally, substitute Log%5B7%5D%287%29+=+1
1%2B2Log%5B7%5D%28x%29%2B3Log%5B7%5D%28y%29-Log%5B7%5D%28z%29