SOLUTION: f(x)=log base b(x) the point contained in the function is (1/8,-3) find b.

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Question 380362: f(x)=log base b(x)
the point contained in the function is (1/8,-3)
find b.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=log%28b%2C+%28x%29%29
If the point (1/8, -3) is on the graph of f(x), then it must fit the equation:
-3+=+log%28b%2C+%281%2F8%29%29
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.

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:
1%2F8+=+b%5E%28-3%29
From this and the facts that
  • 2%5E3+=+8, and
  • negative exponents mean reciprocals
we can determine that b must be 2!