SOLUTION: log[3/5]+3log[15/2]-log[81/8] <all in base 5>

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Question 1210711: log[3/5]+3log[15/2]-log[81/8]
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(54018) About Me  (Show Source):
Answer by greenestamps(13382) About Me  (Show Source):
You can put this solution on YOUR website!


log[3/5]+3log[15/2]-log[81/8]

Use a combination of basic rules of logarithms:

log%28%28A%29%29%2Blog%28%28B%29%29=log%28%28AB%29%29
log%28%28A%29%29-log%28%28B%29%29=log%28%28A%2FB%29%29
b%2Alog%28%28A%29%29=log%28%28A%5Eb%29%29

log%28%283%2F5%29%29%2B3log%28%2815%2F2%29%29-log%28%2881%2F8%29%29
log%28%28%28%283%2F5%29%2A%2815%2F2%29%5E3%29%2F%2881%2F8%29%29%29

Simplify the expression in parentheses.



So the given expression is equivalent to

log%28%2825%29%29

The statement of the problem says all the logarithms are base 5, so

ANSWER: log%285%2C25%29 = 2