You can put this solution on YOUR website! Solve ln(5-x) = 12.
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Find the anti-log (e^) of both sides
5 - x = 162754.7914
-x = 162754.7914 - 5
-x = 162749.7914
x = -16749.7914
:
Check on a good calc: enter: ln(5-(-16749.7914)) = 12
You can put this solution on YOUR website! I agree with the solution by ankor (Carl). Here's another way of looking at it:
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Given:
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This equation can be solved by converting the logarithmic form to the exponential
form. This conversion is defined by the equation:
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In which a is the base of the logarithm. By definition this logarithmic form is equivalent
to the exponential form:
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By comparing the logarithmic form to the given problem you can see that N = (5 x) and
y = 12. The value of a is not quite as straightforward. Natural logarithms, designated by
the use of ln is equivalent to log to the base e in which e = 2.718181828. So
a = e = 2.718281828. If you substitute these given values into the exponential form
you get:
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Since e = 2.718281828 this equation becomes:
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A scientific calculator can be used to raise e to the 12th power. When you do that you get:
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Adding x to both sides converts this equation to:
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Then subtracting 162754.7914 from both sides results in:
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Check this answer by returning to the original equation and substituting -162749.7914
for x. This results in ln(5-(-162749.7914)) which becomes:
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And using a scientific calculator you can enter 162754.7914 and press the ln key to find
that ln(162754.7914) does in fact equal 12. So the answer for x is correct. It does
equal -162749.7914.
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Hope this helps you to see another way ... transferring from logarithmic form to exponential
form is often a useful method in solving logarithmic equations.
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