SOLUTION: How do I simplify the following: 4 ^ log base 4 of 5

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Question 396429: How do I simplify the following:
4 ^ log base 4 of 5
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Once you understand what logarithms are this problem becomes very easy.

The idea behind logarithms is that it is possible to take any positive number (other than 1) and, if you raise it to the correct power, get any other positive number. For example, it is possible to raise 12 to some power and get 1/2. Or raise 3 to some power and get 153. The tricky part is finding out wht these exponents are. What power of 12 results in 1/2? And what power of 3 results in 153?

Logarithms are used to express these exponents. For example log%2812%2C+%281%2F2%29%29 represents the exponent for 12 that results in 1/2. And log%283%2C+%28153%29%29 represents the exponent for 3 that results in 153.

Now let's look at
4%5Elog%284%2C+%285%29%29
Let's look at just the exponent: log%284%2C+%285%29%29. This is "the exponent for 4 that results in 5" or "the power of 4 that results in 5". And where do we find log%284%2C+%285%29%29? Answer: As an exponent for 4! Since your expression raises 4 to the power of 4 that results in 5, your expression is simply a 5!