SOLUTION: log base 4 of 2048 = How can i solve this problem?

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Question 966301: log base 4 of 2048 =
How can i solve this problem?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39629) About Me  (Show Source):
You can put this solution on YOUR website!
log%284%2C2048%29

Factorize 2048.
1024%2A2=2%5E10%2A2=2%5E11

log%284%2C2048%29
log%284%2C%282%5E11%29%29
log%284%2C2%2A%28%282%5E2%29%5E5%29%29
log%284%2C2%2A%284%5E5%29%29
log%284%2C2%29%2Blog%284%2C%284%5E5%29%29
log%284%2C2%29%2B5

Not sure if you want the decimal approximation for log%284%2C2%29; but "four to what power gives 2"?
...
highlight%281%2F2%2B5%29

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

log base 4 of 2048 =
How can i solve this problem?
log+%284%2C+2048%29+=+x ----- Logarithmic form

4%5Ex+=+2048 -------- Exponential form

4%5Ex+=+2%5E11

%282%5E2%29%5Ex+=+2%5E11

2%5E%282x%29+=+2%5E11

2x = 11 ------- Bases are equal and so are their exponents

x+=+11%2F2, or highlight_green%285%261%2F2%29