document.write( "Question 380362: f(x)=log base b(x)
\n" ); document.write( "the point contained in the function is (1/8,-3)
\n" ); document.write( "find b. \n" ); document.write( "

Algebra.Com's Answer #269967 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"f%28x%29=log%28b%2C+%28x%29%29\"$
\n" ); document.write( "If the point (1/8, -3) is on the graph of f(x), then it must fit the equation:
\n" ); document.write( " $\"-3+=+log%28b%2C+%281%2F8%29%29\"$
\n" ); document.write( "Once you understand what $\"log%28b%2C+%281%2F8%29%29\"$ represents, then it is fairly simple to find b. In general, logarithms are exponents. This specific logarithm represents \"the exponent for b that results in 1/8\". This combined with the fact that the equation tells us that this exponent is -3 makes it possible to figure out b.

\n" ); document.write( "If you haven't figured it out yet, then rewriting the equation in exponential form may help. The general logarithmic equation $\"log%28a%2C+%28p%29%29+=+q\"$ is equivalent to the exponential equation $\"p+=+a%5Eq\"$ . Using this pattern on your equation we get:
\n" ); document.write( " $\"1%2F8+=+b%5E%28-3%29\"$
\n" ); document.write( "From this and the facts that

$\"2%5E3+=+8\"$ , and
negative exponents mean reciprocals

we can determine that b must be 2! \n" ); document.write( "

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