SOLUTION: Write as a single logarithm {{{3log(16,4)+5log(16,v)-8log(16,w)}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Write as a single logarithm {{{3log(16,4)+5log(16,v)-8log(16,w)}}}      Log On


   

Question 130658: Write as a single logarithm


3log%2816%2C4%29%2B5log%2816%2Cv%29-8log%2816%2Cw%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3log%2816%2C4%29%2B5log%2816%2Cv%29-8log%2816%2Cw%29 Start with the given expression


log%2816%2C4%5E3%29%2Blog%2816%2Cv%5E5%29-log%2816%2Cw%5E8%29 Rewrite each log using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29


log%2816%2C64%29%2Blog%2816%2Cv%5E5%29-log%2816%2Cw%5E8%29 Evaluate 4%5E3 to get 64


log%2816%2C%2864%2Av%5E5%29%29-log%2816%2Cw%5E8%29 Combine the logs using the identity log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%29%29

log%2816%2C%2864%2Av%5E5%2Fw%5E8%29%29 Combine the logs using the identity log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29