# Top 39 CAT Logarithms, Surds and Indices Questions With Solutions

CAT Logarithms, Surds and Indices questions are the important questions frequently appearing in the CAT examination. These questions require a solid understanding of fundamental concepts. To help the aspirants, we have compiled all the questions from this topic that appear in the previous CAT papers, along with the video solutions for every question explained in detail by the CAT toppers. One can download them in a PDF format or take them in a test format. Click on the link below to download the CAT Logarithms, Surds and Indices questions with detailed video solutions PDF.

## CAT Logarithms, Surds And Indices Questions Weightage Over Past 5 Years

 Year Weightage 2022 1 2021 3 2020 7 2019 4 2018 7

## CAT Logarithms, Surds and Indices Formulas PDF

Logarithms, surds and indices questions are frequently asked in the previous CAT papers. In order to ace this topic and solve the CAT questions, aspirants must be well-versed in the basic concepts and formulas. To help the aspirants, we have made a PDF which consists of all the formulas, tips and tricks to solve these questions. Every formula in this PDF is very important. Click on the below link to download the CAT Logarithms, Surds and Indices Formulas PDF.

## CAT 2022 Logarithms, Surds and Indices questions

#### Question 1

If $$(\sqrt{\frac{7}{5}})^{3x-y}=\frac{875}{2401}$$ and $$(\frac{4a}{b})^{6x-y}=(\frac{2a}{b})^{y-6x}$$, for all non-zero real values of a and b, then the value of $$x+y$$ is

## CAT 2021 Logarithms, Surds and Indices questions

#### Question 1

For a real number a, if $$\frac{\log_{15}{a}+\log_{32}{a}}{(\log_{15}{a})(\log_{32}{a})}=4$$ then a must lie in the range

#### Question 2

If $$\log_{2}[3+\log_{3} \left\{4+\log_{4}(x-1) \right\}]-2=0$$ then 4x equals

#### Question 3

If $$5 - \log_{10}\sqrt{1 + x} + 4 \log_{10} \sqrt{1 - x} = \log_{10} \frac{1}{\sqrt{1 - x^2}}$$, then 100x equals

## CAT 2020 Logarithms, Surds and Indices questions

#### Question 1

If Y is a negative number such that $$2^{Y^2({\log_{3}{5})}}=5^{\log_{2}{3}}$$, then Y equals to:

#### Question 2

If $$\log_{a}{30}=A,\log_{a}({\frac{5}{3}})=-B$$ and $$\log_2{a}=\frac{1}{3}$$, then $$\log_3{a}$$ equals

#### Question 3

The value of $$\log_{a}({\frac{a}{b}})+\log_{b}({\frac{b}{a}})$$, for $$1<a\leq b$$ cannot be equal to

#### Question 4

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

#### Question 5

If $$x=(4096)^{7+4\sqrt{3}}$$, then which of the following equals to 64?

#### Question 6

If $$\log_{4}{5}=(\log_{4}{y})(\log_{6}{\sqrt{5}})$$, then y equals

#### Question 7

$$\frac{2\times4\times8\times16}{(\log_{2}{4})^{2}(\log_{4}{8})^{3}(\log_{8}{16})^{4}}$$ equals

## CAT 2019 Logarithms, Surds and Indices questions

#### Question 1

If $$(5.55)^x = (0.555)^y = 1000$$, then the value of $$\frac{1}{x} - \frac{1}{y}$$ is

#### Question 2

The real root of the equation $$2^{6x} + 2^{3x + 2} - 21 = 0$$ is

#### Question 3

If m and n are integers such that $$(\surd2)^{19} 3^4 4^2 9^m 8^n = 3^n 16^m (\sqrt{64})$$ then m is

#### Question 4

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

## CAT 2018 Logarithms, Surds and Indices questions

#### Question 1

If x is a positive quantity such that $$2^{x}=3^{\log_{5}{2}}$$. then x is equal to

#### Question 2

If $$\log_{12}{81}=p$$, then $$3(\dfrac{4-p}{4+p})$$ is equal to

#### Question 3

If N and x are positive integers such that $$N^{N}$$ = $$2^{160}\ and \ N{^2} + 2^{N}\$$ is an integral multiple of $$\ 2^{x}$$, then the largest possible x is

#### Question 4

$$\frac{1}{log_{2}100}-\frac{1}{log_{4}100}+\frac{1}{log_{5}100}-\frac{1}{log_{10}100}+\frac{1}{log_{20}100}-\frac{1}{log_{25}100}+\frac{1}{log_{50}100}$$=?

#### Question 5

If p$$^{3}$$ = q$$^{4}$$ = r$$^{5}$$ = s$$^{6}$$, then the value of $$log_{s}{(pqr)}$$ is equal to

#### Question 6

Given that $$x^{2018}y^{2017}=\frac{1}{2}$$, and $$x^{2016}y^{2019}=8$$, then value of $$x^{2}+y^{3}$$ is

#### Question 7

If $$\log_{2}({5+\log_{3}{a}})=3$$ and $$\log_{5}({4a+12+\log_{2}{b}})=3$$, then a + b is equal to

## CAT 2017 Logarithms, Surds and Indices questions

#### Question 1

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

#### Question 2

If x is a real number such that $$\log_{3}5= \log_{5}(2 + x)$$, then which of the following is true?

#### Question 3

The value of $$\log_{0.008}\sqrt{5}+\log_{\sqrt{3}}81-7$$ is equal to

#### Question 4

If $$9^{2x-1}-81^{x-1}=1944$$, then $$x$$ is

#### Question 5

If $$9^{x-\frac{1}{2}}-2^{2x-2}=4^{x}-3^{2x-3}$$, then $$x$$ is

#### Question 6

If $$log(2^{a}\times3^{b}\times5^{c} )$$is the arithmetic mean of $$log ( 2^{2}\times3^{3}\times5)$$, $$log(2^{6}\times3\times5^{7} )$$, and $$log(2 \times3^{2}\times5^{4} )$$, then a equals

## CAT 2006 Logarithms, Surds and Indices questions

#### Question 1

If $$log_y x = (a*log_z y) = (b*log_x z) = ab$$, then which of the following pairs of values for (a, b) is not possible?

#### Question 2

If x = -0.5, then which of the following has the smallest value?

#### Question 3

Which among $$2^{1/2}, 3^{1/3}, 4^{1/4}, 6^{1/6}$$, and $$12^{1/12}$$ is the largest?

## CAT 2005 Logarithms, Surds and Indices questions

#### Question 1

If x >= y and y > 1, then the value of the expression $$log_x (x/y) + log_y (y/x)$$ can never be

## CAT 2004 Logarithms, Surds and Indices questions

#### Question 1

Let $$u = ({\log_2 x})^2 - 6 {\log_2 x} + 12$$ where x is a real number. Then the equation $$x^u = 256$$, has

## CAT 2003 Logarithms, Surds and Indices questions

#### Question 1

If $$log_3 2, log_3 (2^x - 5), log_3 (2^x - 7/2)$$ are in arithmetic progression, then the value of x is equal to

## CAT 2002 Logarithms, Surds and Indices questions

#### Question 1

If $$f(x) = \log \frac{(1+x)}{(1-x)}$$, then f(x) + f(y) is

## CAT 1997 Logarithms, Surds and Indices questions

#### Question 1

If $$\log_{2}{\log_{7}{(x^2 - x+37)}}$$ = 1, then what could be the value of ‘x’?

#### Question 2

Which of the following is true?

## CAT 1996 Logarithms, Surds and Indices questions

#### Question 1

Find the value of $$\frac{1}{1 + \frac{1}{3-\frac{4}{2+\frac{1}{3-\frac{1}{2}}}}}$$ + $$\frac{3}{3 - \frac{4}{3+\frac{1}{2-\frac{1}{2}}}}$$

## CAT 1991 Logarithms, Surds and Indices questions

#### Question 1

$$2^{73}-2^{72}-2^{71}$$ is the same as