Prove that `log_(b^2) a * log_(c^2) b * log_(a^2) c =1/8`

Show that log_(b)a log_(c)b log_(a)c=1

a=y^(2),b=z^(2),c=x^(2) then prove that log_(a)x^(3)*log_(b)y^(3)*log_(c)z^(3)=(27)/(8)

Given that log_(2)a=s,log_(4)b=5^(2) and log_(c^(2))(8)=(2)/(s^(3)+1) Write (log_(2)(a^(2)b^(3)))/(c^(4)) as a function of 's' (a,b,c>0,c!=1)

Given a^2+b^2=c^2 . Prove that log_(b+c)a+log_(c-b)a=2 log_(c+b)a.log_(c-b)a,forallagt0,ane1 c-bgt0 , c+bgt0 c-bne1 , c+bne1 .

4.Prove that log_(a)(bc).log_(b)(ca).log_(c)(ab)=2+log_(a)(bc)+log_(b)(ca)+log_(c)(ab)

If log_(b) a. log_(c ) a + log_(a) b. log_(c ) b + log_(a) c. log_(b) c = 3 (where a, b, c are different positive real number ne 1 ), then find the value of a b c.

( Prove that )/(1+log_(b)a+log_(b)c)+(1)/(1+log_(c)a+log_(c)b)+(1)/(1+log_(a)b+log_(a)c)=1

Given log_(2) a = s, log_(4) b = s^(2)" and " log_(c^(2)) (8) = 2/(s^(3) + 1) .Write log_(2). (a^(2)b^(2))/c^(4) as a function of 's' (a,b,c, gt 0, c ne 1) .

The minimum value of 'c' such that log_(b)(a^(log_(2)b))=log_(a)(b^(log_(2)b)) and log_(a) (c-(b-a)^(2))=3 , where a, b in N is :