document.write( "Question 93358This question is from textbook Algebra and Trigonometry
\n" ); document.write( ": Find the number: log lower case5 (1/5) \n" ); document.write( "
Algebra.Com's Answer #67991 by bucky(2189)\"\" \"About 
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You are given a log. Set it equal to y and the problem becomes:
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\n" ); document.write( "\"log%285%2C%281%2F5%29%29+=+y\"
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\n" ); document.write( "Change this from logarithmic form to exponential form using the rule:
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\n" ); document.write( "\"log%28b%2CN%29+=+a\" is equivalent to the exponential form \"b%5Ea+=+N\"
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\n" ); document.write( "By comparing the log format of this rule to your given problem, you can see that a = y, b = 5 because
\n" ); document.write( "5 is the base of the given log, and \"N=1%2F5\". Substitute these values into their appropriate
\n" ); document.write( "position in the exponential form to get:
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\n" ); document.write( "\"5%5Ey+=+1%2F5\"
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\n" ); document.write( "Notice on the right side that \"1%2F5\" is equal to \"1%2F5%5E1\". But a number in the denominator
\n" ); document.write( "can be moved up into the numerator if you change the sign of its exponent. So you can say
\n" ); document.write( "that \"1%2F5%5E1+=+5%5E%28-1%29\". That being the case, you can replace \"1%2F5\" with \"5%5E%28-1%29\"
\n" ); document.write( "to make the exponential equation become:
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\n" ); document.write( "\"5%5Ey+=+5%5E%28-1%29\"
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\n" ); document.write( "Notice that 5 is the base on both the left and right sides. So for the two sides to be equal
\n" ); document.write( "their exponents must be equal. Therefore, you know that y = -1.
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\n" ); document.write( "Now recall that at the beginning of this problem we said that
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\n" ); document.write( "\"log%285%2C%281%2F5%29%29+=+y\"
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\n" ); document.write( "Now we know that y = -1 so that we can write this equation as:
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\n" ); document.write( "\"log%285%2C%281%2F5%29%29+=+-1\"
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\n" ); document.write( "and that's the answer to the problem.
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\n" ); document.write( "Hope this has helped you a little to understand the problem and how to work it. The ability
\n" ); document.write( "to translate from the logarithmic to the exponential form and also from the exponential
\n" ); document.write( "form back to the logarithmic form is a useful thing to know. It comes up quite often in
\n" ); document.write( "working problems involving logarithms. \n" ); document.write( "
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