Question 71654
{{{log(x) = log(2x^2) -2}}}
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I'm going to assume that the base of log is 10 for this problem.
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For the time being let's just work on {{{log(2x^2)}}}. I presume you know the rules 
of logarithms.  {{{log(2x^2)}}} equals {{{(log(2x)+ log(x))}}} and furthermore,
{{{log(2x)= log(2)+log(x)}}}
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So putting this expansion all together:
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{{{log(2x^2) = log(2)+log(x)+log(x)}}}
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Substituting this into the original problem for the term {{{log(2x^2)}}} results in:
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{{{ log(x) = log(2)+log(x)+log(x)-2}}}
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On the right side, combining the two {{{log(x)}}} terms gives us:
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{{{log(x) = log(2) + 2log(x) - 2}}}
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Subtract {{{2log(x)}}} from both sides leaves us with:
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{{{-log(x) = log(2) - 2}}}
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Multiply both sides by -1:
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{{{log(x) = -log(2) + 2}}}
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Using a calculator you can find log(2) and subtract it from 2.  The answer is 1.698970004.
So the equation is now:
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{{{log(x) = 1.698970004}}}
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Convert this to exponential form to find that:
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{{{x = 10^1.698970004 = 50}}}
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The answer is that x = 50, but you can track the work and cut it off at the point
that you think satisfies the "exact form" asked for in the problem.
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Next problem:
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{{{ln(4) - ln(x) = 20}}}
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Subtract {{{ln(4)}}} from both sides to get:
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{{{-ln(x) = -ln(4) + 20}}}
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Multiply the entire equation by -1
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{{{ln(x) = ln(4)-20}}}
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This time the base is {{{e}}}.
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Use a calculator to find ln(4) and once you get that, subtract 20. The result should be
-18.61370564. This makes the equation:
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{{{ln(x) = -18.61370564}}}
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Convert this to exponential form by raising {{{e}}} to the power -18.61370564 on your calculator.
The answer you should get is 
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{{{x= (8.24461449)*(10^(-9))}}}
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Hope this helps you with your understanding of logarithms.