If `4^A+9^B=10^C ,` where `A=(log)_(16)4,B=(log)_3 9, C=(log)_x 83` then find `x`.

Solve for x :(log)_4(log)_3(log)_2x=0

Find the value of 49^A+5^B where A=1-(log)_7 2, B=-(log)_5 4.

Solve (log)_x2(log)_(2x)2=(log)_(4x)2.

If log_2 log_3 log_4 (x+1) =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

If 3^x=4^(x-1) , then x= , (a) (2(log)_3 2)/(2(log)_3 2-1) (b) 2/(2-(log)_2 3) (c) 1/(1-(log)_4 3) (d) (2(log)_2 3)/(2(log)_2 3-1)

If x=1+(log)_a b c , y=1+(log)_b c a and z=1+(log)_c a b , then prove that x y z=x y+y z+z x

Given system of simultaneous equations 2^x\ . 5^y=1\ a n d\ 5^(x+1). 2^y=2. Then - (a) . x=(log)_(10)5\ a n d\ y=(log)_(10)2 (b) . x=(log)_(10)2\ a n d\ y=(log)_(10)5 (c) . x=(log)_(10)(1/5)\ a n d\ y=(log)_(10)2 (d) . x=(log)_(10)5\ a n d\ y=(log)_(10)(1/2)

If log ((x+y)/3)=1/2 (log x +log y) then find the value of x/y+y/x

Prove that a^x-b^y=0 where x=sqrt((log)_a b), y=sqrt((log)_b a), a >0, b >0 , a , b!=1