SOLUTION: Evaluate the following expression without using a calculator. {{{8^log(8,(19))}}}

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Question 1043282: Evaluate the following expression without using a calculator.
8%5Elog%288%2C%2819%29%29
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
8%5Elog%288%2C%2819%29%29

log%28b%2C%28a%29%29 means 

"the exponent to which we must raise 'b' to get 'a'"

That's why log%285%2C%2825%29%29=2

It's 2 because 2 is the exponent to which we must raise 5 to get 25.

Your problem 

8%5Elog%288%2C%2819%29%29

says in words:

8 raised to the exponent to which 8 must be raised to get 19.

When you do whatever it is necessary to do in order to accomplish 
a task, you accomplish the task, right?

So when you do to 8 what you must do to 8 to get 19, then you
get 19.

Answer: 19.

Try to think through those words.  It's tricky wording, but it's 
a case of this:

"When you do what you have to do in order to get X, then
you get X."

Edwin

Answer by ikleyn(52803) About Me  (Show Source):