document.write( "Question 283758: Evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. Show your work. Use the resulting ordered pairs to plot the graph. State the equation of the line asymptotic to the graph (if any).\r
\n" ); document.write( "\n" ); document.write( "y= log[5]x
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Algebra.Com's Answer #205976 by jsmallt9(3758) $\"\"$ $\"About$

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As a base 5 logarithm, the only values for y you will be able to find will those for x's that are known powers of 5. 1 is a power of 5. It is $\"5%5E0\"$ . For x's greater than 1 use 5, 25 and 125 (which are powers of 5 should know (or be able to figure out). For x's between 0 and 1 use 1/5, 1/25 and 1/125. But these values will not make the graph easy. It will be hard to graph x values of 25 and 125 on the same graph as x values of 1/25 and 1/125 unless you have an immense piece of graph paper.

\n" ); document.write( "A more practical approach would be to use the base conversion formula, $\"log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29\"$ , to rewrite the base 5 logarithm as an equivalent expression of base 10 logarithms:
\n" ); document.write( " $\"y+=+log%28%28x%29%29%2Flog%28%285%29%29\"$
\n" ); document.write( "Now we can pick any (positive) numbers we want for x and use our calculator to find the value for y. I'll leave that up to you to do.

\n" ); document.write( "For the asymptote, logarithmic functions have a vertical asymptote for the value of x that makes the argument 0. It works like this because arguments of logarithms cannot be zero or negative. So zero represents the highest invalid argument. X must have values that result in arguments greater than zero.

\n" ); document.write( "Your argument is simply x so x=0 (i.e. the y-axis) is a vertical asymptote for the graph of your function. \n" ); document.write( "

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