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question about a logarithmic funtion using only variables

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3 Answers

Sorry, but this answer is wrong.  The exponent (cx+d) applies only to the b; the a is not part of the base.  So taking the base (ab) logarithm is the wrong move.  George C's answer, complicated as it is, is correct.


This "answer" was not intended as an answer to the problem, but as a comment on Casey V's answer.

(h - k)/a  =  b^(cx + d)

ln ((h - k)/a) =  (cx + d) ln b

(ln ((h - k)/a)/ln b) = cx + d

 (ln ((h - k)/a)/ln b)  -  d  =  cx

 ((ln ((h - k)/a)/ln b) - d)/c  =  x 

(((ln ((h - k)/a)))/ln b) - d)/c  =  x