Prove? #log_x(y)xxlog_y(x)=1#
3 Answers
See explanation.
Explanation:
The change of base formula says
Applying that here we have:
By definition of the logarithm we have:
# log_a b = c iff a^c=b #
If we apply the definition to
# log_xy = Aiff x^A= y#
And if we apply the definition to
# log_yx =B iff y^B = x #
And if we replace
# (y^B)^A= y iff y^(AB)= y iff AB =1 #
And the result follows, as:
# AB =1 iff log_xy \ log_yx =B = 1# QED
See below
Explanation:
There are a couple of ways to do this:
- Use the log base switch rule:
#log_a(b)=1/log_b(a)#
- Use the log base change rule:
#log_a(b)=log_x(b)/log_x(a)#