SOLUTION: EVALUATE 5 log(13) exp3rt169 I know the answer but I need the steps. The answer is 10/3

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Question 416442: EVALUATE 5 log(13) exp3rt169
I know the answer but I need the steps. The answer is 10/3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5%2Alog%2813%2C%28root%283%2C169%29%29%29


5%2Alog%2813%2C%28%28169%29%5E%281%2F3%29%5E%22%22%29%29


5%281%2F3%29%2Alog%2813%2C%28169%29%29


%285%2F3%29%2Alog%2813%2C%28169%29%29


%285%2F3%29%2Alog%2813%2C%2813%5E2%29%29


%285%2F3%29%282%29%2Alog%2813%2C%2813%29%29


%2810%2F3%29%2Alog%2813%2C%2813%29%29


%2810%2F3%29%2A%281%29


10%2F3


So 5%2Alog%2813%2C%28root%283%2C169%29%29%29=10%2F3


Notes:

1) log%28b%2C%28b%29%29=1 where b%3E0, b%3C%3E1 or b%3C%3E0. So this means that log%2813%2C%2813%29%29=1

2) I'm also using the formula log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29. In other words, we can pull down the exponent and place it out front as a coefficient.


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Jim