CAT Exponents and Logarithms Questions are one of the most commonly tested topics in CAT exam. Questions from Exponents and Logarithms have appeared consistently in the CAT exam for the last several years. Questions from Exponents and Logarithms range from very easy to very hard. The basic concept is very easy, learn the concepts and practice a wide range of CAT Questions from 2IIM. One can usually expect 2-3 questions from Logarithms and Exponents in the CAT exam. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.
If log_{2}X + log_{4}X = log_{0.25}√6 and x > 0, then x is
log_{9} (3log_{2} (1 + log_{3} (1 + 2log_{2}x))) = \\frac{1}{2}\\). Find x.
If 2^{2x+4} – 17 × 2^{x+1} = –4, then which of the following is true?
If log_{12}27 = a, log_{9}16 = b, find log_{8}108.
\\frac{log_3(x-3)}{log_3(x-5)}\\) < 0. If a, b are integers such that x = a, and x = b satisfy this inequation, find the maximum possible value of a – b.
log_{5}x = a (This should be read as log X to the base 5 equals a) log_{20}x = b. What is log_{x}10?
log_{3}x + log_{x}3 = \\frac{17}{4}\\). Find the value of x.
log_{x}y + log_{y}x^{2} = 3. Find log_{x}y^{3}.
If log_{2} 4 * log_{4} 8 * log_{8} 16 * ……………n^{th} term = 49, what is the value of n?
If 3^{3 + 6 + 9 + ……… 3x } = (0.\\overline{037}\\))^{-66}, what is the value of x?
x, y, z are 3 integers in a geometric sequence such that y - x is a perfect cube.
Given, log_{36}x^{2} + log_{6}√y + 3log_{216}y^{1/2}z = 6. Find the value of x + y + z.
10^{log(3 - 10logy)} = log_{2}(9 - 2^{y}), Solve for y.
4^{6+12+18+24+…+6x} = (0.0625)^{-84}, what is the value of x?
The Questions that follow, are from actual CAT papers. If you wish to take them separately or plan to solve actual CAT papers at a later point in time, It would be a good idea to stop here.
If x_{1} = -1 and x_{m} = x_{m + 1} + (m + 1) for every positive integer m, then x_{100} equals
Let log_{a}30 = A, log_{a}\\frac{5}{3}) = -B and log_{2}a = \\frac{1}{3}), then log_{3}a equals
\\frac{2×4×8×16}{(log_{2}4)^{2}(log_{4}8)^{3}(log_{8}16)^{4}}) equals
If a,b,c are non-zero and 14^{a} = 36^{b} = 84^{c}, then 6b(\\frac{1}{c}) - \\frac{1}{a})) is equal to
The value of log_{a}\\frac{a}{b}) + log_{b}\\frac{b}{a}), for 1 < a ≤ b cannot be equal to
If log_{4} 5 = (log_{4} y) (log_{6} √5), then y equals
The number of real-valued solutions of the equation 2^{x} + 2^{-x} = 2 - (x - 2)^{2} is
If x = (4096)^{7+4√3}, then which of the following equals 64?
If y is a negative number such that 2^{y2log35} = 5^{log23}, then y equals
The real root of the equation 2^{6x} + 2^{3x+2} - 21 = 0 is
If x is a real number ,then \\sqrt{log_{e}\frac{4x - x^2}{3}}) is a real number if and only if
If 5^{x} – 3^{y} = 13438 and 5^{x-1} + 3^{y+1} = 9686 , then x+y equals [TITA]
If (5.55)^{x} = (0.555)^{y} = 1000, then the value of \\frac{1}{x}) - \\frac{1}{y}) is
If m and n are integers such that (\\sqrt{2}))^{19} 3^{4} 4^{2} 9^{m} 8^{n} = 3^{n} 16^{m} (∜64) then m is
Let x and y be positive real numbers such that log_{5}(x + y) + log_{5}(x - y) = 3, and log_{2}y - log_{2}x = 1 - log_{2}3. Then xy equals
If p^{3} = q^{4} = r^{5} = s^{6}, then the value of log_{s} (pqr) is equal to
\\frac{1}{log_{2}100}\\) - \\frac{1}{log_{4}100}\\) + \\frac{1}{log_{5}100}\\) - \\frac{1}{log_{10}100}\\) + \\frac{1}{log_{20}100}\\) - \\frac{1}{log_{25}100}\\) + \\frac{1}{log_{50}100}\\) = ?
If x is a positive quantity such that 2^{x} = 3^{log52} , then x is equal to
If log_{12}81 = p, then 3(\\frac{4 - p}{4 + p})) is equal to:
Given that x^{2018} y^{2017} = 1/2 and x^{2016} y^{2019} = 8, the value of x^{2} + y^{3} is
If log_{2}(5 + log_{3}a) = 3 and log_{5}(4a + 12 + log_{2}b) = 3, then a + b is equal to
If x is a real number such that log_{3}5 = log_{5}(2 + x), then which of the following is true?
If 9^{x - (\\frac{1}{2}))} – 2^{2x – 2} = 4^{x} – 3^{2x – 3}, then x is
If log(2^{a} × 3^{b} × 5^{c}) is the arithmetic mean of log(2^{2} × 3^{3} × 5), log(2^{6} × 3 × 5^{7}), and log(2 × 3^{2} × 5^{4}), then a equals [TITA]
Suppose, log_{3}x = log_{12}y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log_{6}G is equal to:
The value of log_{0.008}√5 + log_{√3}81 – 7 is equal to:
If 9^{2x – 1} – 81^{x-1} = 1944, then x is
The Questions that follow, are from actual XAT papers. If you wish to take them separately or plan to solve actual XAT papers at a later point in time, It would be a good idea to stop here.
What is the remainder if 19^{20} – 20^{19} is divided by 7?
If \\sqrt[3]{7^{a} \times(35)^{b+1} \times(20)^{c+2}}) is a whole number then which one of the statements below is consistent with it?
\\frac{\log (97-56 \sqrt{3})}{\log \sqrt{7+4 \sqrt{3}}}) equals which of the following?
If \x^{2}+x+1=0, \text { then } x^{2018}+x^{2019}) then equals which of the following:
The Questions that follow, are from actual IPMAT papers. If you wish to take them separately or plan to solve actual IPMAT papers at a later point in time, It would be a good idea to stop here.
Given A = 2^{65} and B = (2^{64} + 2^{63} + 2^{62} + ... + 2^{0}), which of the following is true?
If log 2, log (2x - 1) and log (2x + 3) are in A.P, then x is equal to ____
The value of 0.04^{log√5(\\frac{1}{4}) + \\frac{1}{8}) + \\frac{1}{16}))} is __________.
If log_{5}log_{8}(x^{2} - 1) = 0, then a possible value of x is
Suppose that a, b, and c are real numbers greater than 1. Then the value of \\frac{1}{1+\log _{a^{2} b} \frac{c}{a}}+\frac{1}{1+\log _{b^{2} c} \frac{a}{b}}+\frac{1}{1+\log _{c^{2} a} \frac{b}{c}}\\) is
If x, y, z are positive real numbers such that x^{12} = y^{16} = z^{24},and the three quantities 3log_{y}x, 4log_{z}y, nlog_{x}z are in arithmetic progression, then the value of n is
The inequality \\log _{2} \frac{3x - 1}{2 - x} < 1\\) holds true for
The set of values of x which satisfy the inequality 0.7^{2x2 - 3x + 4} < 0.343 is
The value of \\log _{3} 30^{-1} + \log _{4} 900^{-1} + \log _{5} 30^{-1}\\) is
The inequality \\log _{a}{f(x)} < \log _{a}{g(x)}\\) implies that
Determine the greatest number among the following four numbers
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