You can put this solution on YOUR website! Given:
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By the rules of logarithms, subtracting two logarithms is the same as the logarithm
of their quotient. So:
is equivalent to
.
Substitute this into the given equation and you have:
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On the right side note that by the rules of logarithms the multiplier of a logarithm
can be used as the exponent of the quantity that the logarithm operates on. In other words:
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Replace the right side of the equation with this equivalent form and you have:
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Each side of this equation has the ln operator acting on a quantity. In order for the
equation to be true the quantity on each side must be equal so that the ln operator
acts on it to give the same answer on each side. This means:
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Get rid of the x in the denominator by multiplying both sides of this equation by x to get:
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Get rid of the x on the left side by subtracting x from both sides:
. which is the same as
.
Solve for x by dividing both sides by 3 (the multiplier of x) and you end up with:
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To check this answer, plug +1 in for x in the original equation that you were given and
you have:
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and this reduces to:
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Using a calculator you can find that ln(4) = 1.386294361, ln(1) = 0, and ln(2) = 0.69314718.
Substituting these values results in:
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If you multiply out the right side the equation becomes:
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So the answer of x = 1 is correct.
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Hope this helps you to understand the problem and how you can use some basic rules of
logarithms to determine the answer.
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