SOLUTION: Please check my answers Evaluate the expression: log(base 2) 72 - log(base 2) 9 My answer: log(base 2)(72/9) ----------- ----------- ----------- ----------- -----------

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please check my answers Evaluate the expression: log(base 2) 72 - log(base 2) 9 My answer: log(base 2)(72/9) ----------- ----------- ----------- ----------- -----------       Log On


   

Question 914997: Please check my answers
Evaluate the expression:
log(base 2) 72 - log(base 2) 9
My answer: log(base 2)(72/9)
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Evaluate the expression:
log(1/√1000)
My answer: log(1)-log(10√10)
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Evaluate the expression:
log(base 2) 225 − log(base 2) 20 − log(base 2) 45
log(base 2)(225/20-45) or rather log(base 2)(225/25) ? I don't think this is right, not sure.
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Use the Laws of Logarithms to expand the expression:
ln(z)
This one I have no idea how to solve.
Please help. Thanks!
Found 4 solutions by Fombitz, ewatrrr, MathLover1, MathTherapy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C%2872%2F9%29%29 is not simplified.
72 is divisible by 9.
The answer is also a factor of 2.
.
.
.
Can be further simplified.
sqrt%281000%29=1000%5E%281%2F2%29
If you take the log of both sides,
log%28%28sqrt%281000%29%29%29=%281%2F2%29log%28%281000%29%29
.
.
.
No, it's not.
log%28%28a%29%29-log%28%28b%29%29-log%28%28c%29%29=log%28%28a%2Fb%29%29-log%28%28c%29%29
log%28%28a%29%29-log%28%28b%29%29-log%28%28c%29%29=log%28%28a%2F%28bc%29%29%29
.
.
What is z??

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Evaluate
log%282%2C+72%2F9%29+=+log%282+%2C+8%29 = 3
Note : 2^3 = 8
.........

Log(1) - 1/2log(1000) = 0 - (1/2)3 = -3/2
Note: 1 = 10^0 and 1000 = 10^3
.......
log%282%2C+225%2F%2820%2A45%29%29+=+log%282%2C+225%2F900%29+=+log%282%2C+1%2F4%29 = -2
Note: 2^(-2) = 1/4
.....
Use the Laws of Logarithms to expand the expression:
ln(z) = x, then e^x = z

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
log%28+2%2C72%29+-+log%28+2%2C9+%29

log%28+2%2C72%2F9%29+
=log%28+2%2C8%29+ ...in base 10 we will have
=log%288%29%2Flog%282%29+
=log%282%5E3%29%2Flog%282%29+
=3log%282%29%2Flog%282%29+
=3log%282%29%2Flog%282%29+
=3cross%28log%282%29%29%2Fcross%28log%282%29%29+

=3+
----------------------------------------


+log%281%2Fsqrt%281000%29%29+
=log%281%2Fsqrt%2810%5E3%29%29
=log%281%2F10sqrt%2810%29%29
=log%281%29-log%2810sqrt%282%2A5%29%29
=log%281%29-log%2810%28sqrt%282%29sqrt%285%29%29%29+
=log%281%29-%28log%282%2A5%29%2Blog%28sqrt%282%29%29%2Blog%28sqrt%285%29%29%29+
=0-%28log%282%29%2Blog%285%29%2Blog%28sqrt%282%29%29%2Blog%28sqrt%285%29%29%29+
if you calculate all above, final result will be:
-3.4538776
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log%28+2%2C+225%29+-+log%28+2%2C+20%29+-log%28+2%2C+45%29+
=log%28+2%2C+225%2F20%29+-log%28+2%2C+45%29+
=log%28+2%2C+%28225%2F20%29%2F45%29+
=log%28+2%2C+%28cross%28225%295%2F20%29%2Fcross%2845%291%29+
=log%28+2%2C+%285%2F20%29%29+
=log%28+2%2C+%28cross%285%291%2Fcross%2820%294%29%29+
=log%28+2%2C+%281%2F4%29%29+
=log%28%281%2F4%29%29%2Flog%282%29+
=%28log%281%29-log%284%29%29%2Flog%282%29+
=%28log%281%29-log%282%5E2%29%29%2Flog%282%29+ ...log%281%29=0
=%28-log%282%5E2%29%29%2Flog%282%29+
=%28-2log%282%29%29%2Flog%282%29+
=-2cross%28log%282%29%29%2Fcross%28log%282%29%29+
=-2+










Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!
Please check my answers

Evaluate the expression:
log(base 2) 72 - log(base 2) 9
My answer: log(base 2)(72/9)

Answer, simplified: highlight_green%283%29
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Evaluate the expression:
log(1/√1000)
My answer: log(1)-log(10√10)
Needs to be completed, as follows:
log+1+-+log+10%28sqrt%2810%29%29

log+1+-+%28log+10+%2A+sqrt%2810%29%29

log+1+-+%28log+10+%2B+log+%28sqrt%2810%29%29%29

highlight%28log+1+-+%28log+10+%2B+log+10%5E%281%2F2%29%29%29

log+1+-+%28log+10+%2B+%281%2F2%29+%2A+log+10%29

Since log 1 = 0, and log 10 = 1, then:

log+1+-+%28log+10+%2B+%281%2F2%29+%2A+log+10%29 becomes: 

0+-+%281+%2B+%281%2F2%29+%2A+1%29_______0+-+%281+%2B+1%2F2%29_______highlight_green%28highlight_green%28-+1%261%2F2%29%29%29, or highlight_green%28-+1.5%29%29

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Evaluate the expression:
log(base 2) 225 − log(base 2) 20 − log(base 2) 45
log(base 2)(225/20-45) or rather log(base 2)(225/25) ? I don't think this is right, not sure.

log+%282%2C+225%29+-+log+%282%2C+20%29+-+log+%282%2C+45%29.
This simplifies to: highlight_green%28-+2%29
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Use the Laws of Logarithms to expand the expression:
ln(z)

Seems to be incomplete.