SOLUTION: log base 4 of 8=

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Question 1011871: log base 4 of 8=
Found 3 solutions by ikleyn, josgarithmetic, MathTherapy:
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
log base 4 of 8 ?
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log%284%2C8%29 = %281%2F2%29%2Alog%282%2C8%29   <-----  because 4 = 2%5E2

= %281%2F2%29%2A3 = 3%2F2.


Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Choose a different base that you would like.

log%284%2C8%29=log%2810%2C8%29%2Flog%2810%2C4%29----Using the Change of Base Formula

0.90308%2F0.60205
highlight%281.5%29--------This suggests maybe Change of Base was not needed.



Try starting with the exponential form of your originally given equation:
4%5Ex=8
%282%5E2%29%5Ex=2%5E3
2%5E%282x%29=2%5E3
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Do you see these are the same base raised to powers, and that if set as equal, their exponents are equal?
2x=3
2x%281%2F2%29=3%281%2F2%29
highlight%28x=3%2F2%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

log base 4 of 8=
log+%284%2C+8%29

log+%282%2C+8%29%2Flog%282%2C+4%29 ----- Applying change of base to base 2

highlight_green%283%2F2%29