SOLUTION: How do I simplify: 4^{log [2^(log 5)]} *both logs have a base of 2* Thanks

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How do I simplify: 4^{log [2^(log 5)]} *both logs have a base of 2* Thanks      Log On


   

Question 189102: How do I simplify:
4^{log [2^(log 5)]}
*both logs have a base of 2*
Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember, is one identity that is useful for simplifying logarithms.


So (in this case, b=2 and x=5)


This means that





simplifies to





In other words,


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Now let's simplify



... Rewrite 4 as 2%5E2


... Multiply the exponents.


... Rewrite the inner log using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29


... Square 5 to get 25


... Use the first identity given to simplify


So


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Answer:


This means that