anonymous
  • anonymous
if ln5=a and ln3=b write ln0.12 as an expression in a and b
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
.12=2*3/2*5
sgadi
  • sgadi
0.12=12/10=6/5=2*3/5 ln(2*3/5)=ln2+ln3-ln5=ln2+b-a
anonymous
  • anonymous
sorry that is wrong. \[.12=\frac{2\times 3}{(2\times 5)^2}\]

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anonymous
  • anonymous
actually .12=12/100 but that is the right idea
anonymous
  • anonymous
i mean sgadi has the right method
anonymous
  • anonymous
so ln2+b-a is the answerÉ
anonymous
  • anonymous
not what i get
anonymous
  • anonymous
what you get im lost
anonymous
  • anonymous
ok lets go slow
anonymous
  • anonymous
\[.12=\frac{12}{100}\]
anonymous
  • anonymous
now reduce this to \[\frac{12}{100}=\frac{3}{25}\]
anonymous
  • anonymous
now it is easy
anonymous
  • anonymous
ish
anonymous
  • anonymous
but where does a and b come in
anonymous
  • anonymous
\[ln(\frac{3}{25})=ln(\frac{3}{5^2})\]
anonymous
  • anonymous
not there yet is is coming
anonymous
  • anonymous
\[ln(\frac{3}{5^2})=ln(3)-ln(5^2)\]
anonymous
  • anonymous
=\[ln(3)-2ln(5)\]
myininaya
  • myininaya
ln(12/100)=ln(3/25)=ln3-ln5^2=ln3-2ln5=b-2a
anonymous
  • anonymous
and there is your a and b. \[ln(3)-2ln(5)=a-2b\]
anonymous
  • anonymous
the gimmick was to rewrite these in terms of ln(3) and ln(5)
myininaya
  • myininaya
b=ln3 a=ln5 so its b-2a
anonymous
  • anonymous
thanks you!

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