SOLUTION: If (c,d) is a point on the graph of {{{y=log (b, a)}}}, what point must be on the graph of {{{y=log (1/b, a)}}}?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: If (c,d) is a point on the graph of {{{y=log (b, a)}}}, what point must be on the graph of {{{y=log (1/b, a)}}}?      Log On


   

Question 1111709: If (c,d) is a point on the graph of y=log+%28b%2C+a%29, what point must be on the graph of y=log+%281%2Fb%2C+a%29?
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
(c,d) is a point on the graph so +d+=+log%28b%2C+%28c%29%29+ —> +b%5E%28d%29+=+c+
If you take the reciprocal of the base, b becomes 1/b and the exponent must be negated to obtain c:
+%281%2Fb%29%5E%28-d%29+=+c++ equivalent to +log%281%2Fb%2C%28c%29%29+=+-d+
thus +highlight%28+matrix%281%2C3%2C+%22+%22%2C+%22+%28+c%2C-d%29%22%2C+%22+%22%29+%29++ must be a point on the graph
=============================
Example/sanity check:
+log%2810%2C%28100%29%29+=+2+ because +10%5E2+=+100+
+log%281%2F10%2C+%28100%29%29+=+-2+ because