SOLUTION: I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Laws

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Laws       Log On


   

Question 197092This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Laws of Logarithms
Simplify 4^log base 2(2^ log base 2 of 5) This question is from textbook Algebra and Trigonometry Structure and Method book 2

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