Given `a^2+b^2=c^2, a >0 ; b >0; c >0,\ c-b!=1,\ c+b!=1,\ ` prove that : `(log)_("c"+"b")a+(log)_("c"-"b")a=2(log)_("c"+"b")adot(log)_("c"-"b")a`

If in a right angled triangle, a\ a n d\ b are the lengths of sides and c is the length of hypotenuse and c-b!=1,\ c+b!=1 , then show that (log)_("c"+"b")"a"+(log)_("c"-"b")"a"=2(log)_("c"+"b")adot(log)_("c"-"b")adot

Prove log_(b) 1=0

Prove that, tan((A)/(2)+B)=(c+b)/(c-b)tan((A)/(2))

If a^2+b^2=23 a b , then prove that log((a+b))/5=1/2(loga+logb)dot

Statement I: If a=y^2,\ b=z^2, c=x^2,\ t h e n8(log)_a x^3dot(log)_b y^3dot(log)_c z^3=27 Statement II: (log)_b adot(log)_c b=(log)_c a ,\ also (log)_b a=1/("log"_a b) Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1. Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true

If a, b, c, are positive real numbers and log_(4) a=log_(6)b=log_(9) (a+b) , then b/a equals

Prove that {:[( b+c,a,a), ( b,c+a,b),( c,c,b+a) ]:}

If a,b,c are in HP, then prove that (a+b)/(2a-b)+(c+b)/(2c-b)gt4 .

If b gt 1, x gt 0 and (2x)^(log_(b) 2)-(3x)^(log_(b) 3)=0 , then x is

If a^x=b , b^y=c ,c^z=a and x=(log)_b a^2, y=(log)_c b^3,z=(log)_a c^k , where a,b, c >0 and a , b , c!=1 then k is equal to a. 1/5 b. 1/6 c. (log)_(64)2 d. (log)_(32)2