CAT Previous Year Questions| Logarithms and Exponents

For a real number a, if log15^a+log32^a/(log15a)(log32a)= = 4 then a must lie in the range

If log2^[3 + log3^{4 + log4^{x − 1}}] − 2 = 0 then 4x equals

If x¹ = −1 and x^m = x^m + 1 + (m + 1) for every positive integer m, then x¹⁰⁰ equals

Let loga³⁰ = A, loga⁵³ = −B and log2^a = 1/3, then log3^a equals

2×4×8×16/(log2⁴)²(log4⁸)³(log8¹⁶)⁴ equals

If a,b,c are non-zero and 14^a = 36^b = 84^c, then 6b(1/c − 1/a) is equal to

If log4⁵ = (log4^y) (log6^ √5), then y equals

The number of real-valued solutions of the equation 2^x + 2^−x = 2 − (x − 2)² is

If y is a negative number such that 2^y2log3⁵ = 5^log2³, then y equals

If 5^x – 3^y = 13438 and 5^x-1 + 3^y+1 = 9686 , then x+y equals

If (5.55)^x = (0.555)^y = 1000, then the value of 1/x − 1/y is

Let x and y be positive real numbers such that log⁵(x + y) + log⁵(x − y) = 3, and log²y − log²x = 1 − log2³. Then xy equals

If p³ = q⁴ = r⁵ = s⁶, then the value of logs^ (pqr) is equal to

If x is a real number such that log3⁵ = log5^{2 + x}, then which of the following is true?