SOLUTION: Can you please help me. Evaluate: (log5 20^4)(log20 5^4) I have to show my work. Thank you

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Can you please help me. Evaluate: (log5 20^4)(log20 5^4) I have to show my work. Thank you      Log On


   

Question 167593: Can you please help me.
Evaluate: (log5 20^4)(log20 5^4)
I have to show my work.
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%285%2C%2820%5E4%29%29log%2820%2C%285%5E4%29%29 Start with the given expression


Convert each log using the change of base formula



So for instance log%285%2C%2820%5E4%29%29=log%2810%2C%2820%5E4%29%29%2Flog%2810%2C%285%29%29 and log%2820%2C%285%5E4%29%29=log%2810%2C%285%5E4%29%29%2Flog%2810%2C%2820%29%29



Use the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 to pull the exponents down and place them in front of the logs


Highlight the common terms.


Cancel out the common terms.


%284%2F1%29%2A%284%2F1%29 Simplify


4%2A4 Reduce


16 Multiply


So log%285%2C%2820%5E4%29%29log%2820%2C%285%5E4%29%29=16