SOLUTION: Evaluate this: log (base 2) 35 - log (base 4) 13. I hope my question is clear!

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Question 842219: Evaluate this: log (base 2) 35 - log (base 4) 13.
I hope my question is clear!
Found 3 solutions by ewatrrr, josgarithmetic, Edwin McCravy:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Using base conversion formula  log%28a%2C+p%29+=+log%28b%2Cp%29%2F+%28log%28b%2C+a%29%29+

+log%2810%2C35%29%2F+%28log%2810%2C+2%29%29+ - +log%2810%2C13%29%2F+%28log%2810%2C+4%29%29+

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
log (base 2) 35 - log (base 4) 13

Evaluate log%282%2C35%29-log%284%2C13%29.

Use change of base formula. Choose a base for which you can either find tables of logarithms or for which a handheld calculator will be able to use.

Common Log will be used here.
log%2810%2C35%29%2Flog%2810%2C2%29-%28log%2810%2C13%29%2Flog%2810%2C4%29%29
1.544068%2F0.30103-1.113943%2F0.60206
5.12928-1.850219
3.279 or very very near it.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C%2835%29%29%22%22-%22%22log%284%2C%2813%29%29
Use change of base formula on second term:
log%28A%2C%28C%29%29=log%28B%2C%28C%29%29%2Flog%28B%2C%28A%29%29
log%282%2C%2835%29%29%22%22-%22%22log%282%2C%2813%29%29%2Flog%282%2C%284%29%29
We calculate log%282%2C%284%29%29 by setting it equal to x
log%282%2C%284%29%29%22%22=%22%22x
by using the fact that log%28B%2C%28A%29%29=C is equivalent to B%5EC=A
2%5Ex%22%22=%22%224
2%5Ex%22%22=%22%222%5E2
Equate exponents
x = 2
So log%282%2C%284%29%29%22%22=%22%222
log%282%2C%2835%29%29%22%22-%22%22log%282%2C%2813%29%29%2F2
log%282%2C%2835%29%29%22%22-%22%22expr%281%2F2%29%2Alog%282%2C%2813%29%29
Use the rule A%2Alog%28B%2C%28C%29%29=log%28B%2C%28C%5EA%29%29

matrix%282%2C1%2C%22%22%2Clog%282%2C%2835%29%29%29matrix%282%2C1%2C%22%22%2C%22%22-%22%22%29matrix%282%2C1%2C%22%22%2C%0D%0A%0D%0A%0D%0Alog%282%2C%2813%5E%281%2F2%29%29%29%29
The 1%2F2 power is the same as the square root:
log%282%2C%2835%29%29%22%22-%22%22log%282%2C%28sqrt%2813%29%29%29
Use the rule log%28B%2C%28A%29%29-log%28B%2C%28C%29%29=log%28B%2C%28A%2FC%29%29
log%282%2C%2835%2Fsqrt%2813%29%29%29
Edwin