document.write( "Question 80372: I would like a solution to how it is done to evaluate each expression:
\n" ); document.write( "-2+ 1n e^3. I do know the answer is 1 (from the back of my text book's answers to the problem), but the log calculator on this web site had the answer as 0 because it was needed 0 divisions to get to 1. Please explain .
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Algebra.Com's Answer #57682 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
Given the expression:
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\n" ); document.write( "-2 + ln e^3
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\n" ); document.write( "Simplify this expression.
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\n" ); document.write( "You can just about do this in your head by applying two rules of logarithms. The first rule
\n" ); document.write( "is that if you take the logarithm of a quantity that with an exponent, you can make an equivalent
\n" ); document.write( "term by multiplying the logarithm of the quantity times the exponent. If you apply this
\n" ); document.write( "rule to the given expression, you convert the expression to:
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\n" ); document.write( "-2 + 3*ln e
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\n" ); document.write( "The second rule (actually a definition) is that you can convert a logarithm to exponential
\n" ); document.write( "form by raising the base to the exponent on the other side and setting that equal to
\n" ); document.write( "the quantity you are taking the logarithm of. Easier to do than to say. Let's use this
\n" ); document.write( "rule/definition to find ln e.
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\n" ); document.write( "Let's set y equal to ln e. We know that the base of the natural logarithms is e. If
\n" ); document.write( "we raise that base to the exponent y it will equal the quantity that the ln function
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\n" ); document.write( "ln x = y means (base)^y = x
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\n" ); document.write( "and since the (base) is e we can say e^y = x
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\n" ); document.write( "Now notice that for this problem x is e. Substituting e for x gives us
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\n" ); document.write( "e^y = e
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\n" ); document.write( "If you look at this carefully, you can see that to make the left side equal to the
\n" ); document.write( "right side, the exponent y has to be 1 ... making the equation e^1 = e.
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\n" ); document.write( "So we now know that y = 1, but recall that we had said y = ln e. This tells us that
\n" ); document.write( "1 = ln e
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\n" ); document.write( "Note - you can also do this on a scientific calculator. Fine the function key for e^x.
\n" ); document.write( "Enter 1 for x and then press the e^x key. You should get 2.718281828 as the value of
\n" ); document.write( "e^1 which is the same as e. Then press the ln key to take the natural logarithm of
\n" ); document.write( "2.718281828. You should get 1 as the answer. This tells you that the natural logarithm
\n" ); document.write( "of e (or 2.718281828) is 1 ... just as we found in the previous paragraph.
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\n" ); document.write( "Anyhow, if we go back to the expression in the form:
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\n" ); document.write( "-2 + 3*ln e
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\n" ); document.write( "and we substitute 1 for ln e, we get:
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\n" ); document.write( "-2 + 3*1 = -2 + 3 = +1
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\n" ); document.write( "And that's the book answer.
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\n" ); document.write( "Hope this helps you with your understanding of logarithms in general and natural logarithms
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