What is the sum of ‘n’ terms in the series log m + log (m²/n) + log (m³/n²) + log (m⁴/n³) + …?      (CAT 2002)

If logᵧx = (a . log_z y) = (b . logₓ z) = ab, then which of the following pairs of values for (a, b) is not possible?  (CAT 2006)

If x is real number such that log₃5 = log₅(2 + x), then which of the following is true?    (CAT 2017)

If log(2ᵃ * 3ᵇ * 5ᶜ) is the arithmetic mean of log(2² * 3³ * 5), log(2⁶ * 3 * 5⁷), and log (2 * 3² * 5⁴), then a equals  (CAT 2017)

Suppose, log₃x = log₁₂y = a, where x, y are positive numbers. If G is the geometric mean of x and y, then log₆G is equal to         (CAT 2017)                                                                                                                                        

The value of log₀.₀₀₈ √5 + log_√3 81 – 7 is equal to  (CAT 2017)

If 9²ˣ⁻¹ – 81ˣ⁻¹ = 1944, then x is?        (CAT 2017)

If log₂x · log_x/642 = log_x/162. Then x is  (IIFT 2008)

What is the value of √(a/b)​​, if log₄log₄ 4ᵃ⁻ᵇ = 2log₄ (√a–√b​) + 1        (IIFT 2010)

log₅2 is      (IIFT 2010)