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11 votes
11 votes
Hello, help me please))

Hello, help me please))-example-1
User Rhyshort
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1 Answer

15 votes
15 votes

Answer:

  • 6
  • 9
  • 1/8
  • -10/11

Explanation:

You can rewrite the given log expressions to express them in terms of ln(a), ln(b), and ln(c). Then substituting the given values will produce the value of the expression.

Or, you can define the variables 'a', 'b', and 'c' and let your calculator compute these directly.

__

1.


\ln\left((a^4)/(b^4c^(-2))\right)=4\ln(a)-(4\ln(b)-2\ln(c))=4\cdot2-4\cdot3+2\cdot5=\boxed{6}

2.


\ln\left(\sqrt{b^(-2)c^4a^2}\right)=(1)/(2)\left(-2\ln(b)+4\ln(c)+2\ln(a)\right)=\ln(a)-\ln(b)+2\ln(c)\\\\=2-3+2\cdot5=\boxed{9}

3.


(\ln(a^1b^2))/(\ln(bc)^2)=(\ln(a)+2\ln(b))/((\ln(b)+\ln(c))^2)=(2+2\cdot3)/((3+5)^2)=(8)/(64)=\boxed{(1)/(8)}

4.


\ln(c^(-2))\left(\ln(a)/(b^(-3))\right)^(-1)=(-2\ln(c))/(\ln(a)-(-3)\ln(b))=(-2(5))/(2+3\cdot3)=\boxed{-(10)/(11)}

_____

The applicable rules of logarithms are ...

  • ln(ab) = ln(a) +ln(b)
  • ln(a/b) = ln(a) -ln(b)
  • ln(a^b) = b·ln(a)
  • ln(a) = b ⇔ a = e^b

Of course, a square root is the same as a 1/2 power.

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User Dimuthu
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