Question 380362
{{{f(x)=log(b, (x))}}}
If the point (1/8, -3) is on the graph of f(x), then it must fit the equation:
{{{-3 = log(b, (1/8))}}}
Once you understand what {{{log(b, (1/8))}}} 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.<br>
If you haven't figured it out yet, then rewriting the equation in exponential form may help. The general logarithmic equation {{{log(a, (p)) = q}}} is equivalent to the exponential equation {{{p = a^q}}}. Using this pattern on your equation we get:
{{{1/8 = b^(-3)}}}
From this and the facts that<ul><li>{{{2^3 = 8}}}, and</li><li>negative exponents mean reciprocals</li></ul> we can determine that b must be 2!