if `log 15` base 16 =a and log 18 base 12 = b then show that log 24 base 25 = (5-b)/(16a - 8ab -4b +2 )

If log_(40)4 = a and log_(40)5 = b , then show that log_(40)16=4(1-a-b) .

If a^(2) + b^(2) = 23ab , show that : "log" (a+b)/(5) = (1)/(2) (log a + log b) .

If a^(2) + b^(2) = 7 ab, show that log ((a + b)/(3)) = (1)/(2) (log a + log b ).

If "log" (a-b)/(2) = (1)/(2) (log a + log b), show that : a^(2) + b^(2) = 6ab .

If log 25 = a " and " log 225 = b , then find the value of log ((1/9)^(2)) + log (1/(2250)) in terms of a and b (base of the log is 10 everywhere).

If a^(4) + b^(4) = 14 a^(2)b^(2) , then show that log(a^(2) + b^(2)) = log a + log b + 2 log 2 .

Prove that (log a)^2-(log b)^2=log (ab) log(a/b)

If a=log_(24)12,b=log_(36)24, c=log_(48)36 , then show that 1+abc=2bc

If a=log_(24)12,b=log_(36)24, c=log_(48)36 , then show that 1+abc=2bc