SOLUTION: Rewrite the expression 3 ln(2) - 2 ( ln(10) - ln(4) ) in the form ln(x), a single logarithm I rewrote it as ln(2)^3+ln(4)^2 /ln(10)^2 thus getting the the answer ln(8)+ln(1

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Rewrite the expression 3 ln(2) - 2 ( ln(10) - ln(4) ) in the form ln(x), a single logarithm I rewrote it as ln(2)^3+ln(4)^2 /ln(10)^2 thus getting the the answer ln(8)+ln(1      Log On


   



Question 414454: Rewrite the expression 3 ln(2) - 2 ( ln(10) - ln(4) ) in the form ln(x), a single logarithm
I rewrote it as ln(2)^3+ln(4)^2 /ln(10)^2
thus getting the the answer ln(8)+ln(16)/ln(100)=ln(24/100)
I am told, however, that the correct answer is ln(128/100)
Can you please explain how?

Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Rewrite the expression 3 ln(2) - 2 ( ln(10) - ln(4) ) in the form ln(x), a single logarithm
I rewrote it as ln(2)^3+ln(4)^2 /ln(10)^2
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3 ln(2) - 2 ( ln(10) - ln(4))
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= 3*ln(2) -2(ln(10/4))
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= 3*ln(2)- ln(2.5^2)
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= ln(8) - ln(6.25)
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= ln[8/6.25]
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= ln[1.28]
---
= 0.2469
==================
Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
3%2A+ln%282%29+-+2%2A%28+ln%2810%29+-+ln%284%29+%29
3%2Aln%282%29+-+2%2Aln%2810%29+%2B+2%2Aln%284%29
ln%282%5E3%29+-+ln%2810%5E2%29+%2B+ln%284%5E2%29
ln%28%288%2A16%29%2F100%29
ln%28128%2F100%29
ln%281.28%29
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Just look at the sign change carefully
I think this is OK