SOLUTION: Solve the logarithm: log2(log4 256)

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Question 1001239: Solve the logarithm: log2(log4 256)
Found 3 solutions by MathLover1, addingup, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C%28log%284%2C+256%29%29%29
=log%282%2C%28log%28256%29%2Flog%284%29%29%29
=log%282%2C%28log%28+2%5E8%29%2F2log%282%29%29%29
=log%282%2C%288log%28+2%29%2F2log%282%29%29%29
=log%282%2C%288%2F2%29%29
=log%282%2C%284%29%29
=log%282%2C%282%5E2%29%29
=2

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
First do the calculation inside the parenthesis:
log_4(256)= 4 Now calculate log base 2 of 4:
log_2(4)= 2 This is your answer.
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NOTE: the hand-held calculators I know only calculate natural logarithms (ln) and log base 10 (log).
To calculate a log with a different base you have to use the formula:
log_b%28x%29=+log_d%28x%29%2Flog_d%28b%29.
Let's do one of yours, the one inside parenthesis:
log_4%28256%29=+ln%28256%29%2Fln%284%29=+5.545%2F1.386+=+4 I used 3 decimals to get a more accurate answer.
Now follow this example and do log_2(4). Your result should be 2.
Once you get the hang of it it's really very easy.
J

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve the logarithm: log2(log4 256)
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log%282%2C+%28log%284%2C+%28256%29%29%29%29 = log%282%2C+%28log%284%2C+%284%5E4%29%29%29%29     <----- 256 = 4%5E4

= log%282%2C+%284%29%29              <----- log%284%2C+%284%5E4%29%29 = 4

= 2.