Verified answer

Answer:

proofed..

Step-by-step explanation:

(log×b)(log×a)=(log×a)(log×b).........(*)

Now use the fact that

p log×q =log×(p^q)

For the L.H.S of (*), use p= log×b and q= log×a

For the R.H.S of (*), use p= log×a and q= log×b

This gives, log

[tex] log_{x} \: a log_{x}b \: = log_{x} \: b log_{x}a[/tex]

Now raising x to the power of each of these(i.e. getting rid of the logx from each side) We are left with the required result:

[tex]a log_{x} b \: = b log_{x}a[/tex]

Hope it helps you.