How to solve this problem concerning logarithms?
a, b, c, d are positive real numbers, so that #log_a(b)=3/2# and #log_c(d)=5/4# .
If a-c=9, what is the solution of b-d?
a, b, c, d are positive real numbers, so that
If a-c=9, what is the solution of b-d?
2 Answers
Given:
Raise both sides of both equation to their respective bases:
Substitute
Subtract equation [2.1] from equation [1.2]:
(see Douglas K's answer for the question as stated, however...)
If
Explanation:
and if
Similarly,
and if
We are given that
If
then the only possibility is
and
and from there:
and