# CAT Practice : Exponents and Logarithms

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The following topics are covered in the CAT quant section from Arithmetic in Exponents and Logarithms. Detailed explanatory answers, solution videos and slide decks are also provided.
1. ### Logarithm - Inequalities

If log2X + log4X = log0.25$\sqrt {6}$> and x > 0, then x is

1. 6-1/6
2. 61/6
3. 3-1/3
4. 61/3
6-1/6
• Logarithm - Inequalities
• Medium
2. ### Logarithm - Simple

log9 (3log2 (1 + log3 (1 + 2log2x))) = ${1 \over 2}$. Find x.

1. 4
2. ${1 \over 2}$
3. 1
4. 2
3. ### Logartihm - Quadratic Equations

If 22x+4 – 17 × 2x+1 = –4, then which of the following is true?

1. x is a positive value
2. x is a negative value
3. x can be either a positive value or a negative value
4. None of these
x can be either a positive value or a negative value
• Easy
4. ### Logartihm - Algebra

If log1227 = a, log916 = b, find log8108.

1. ${2(a + 3) \over 3b}$
2. ${2(a + 3) \over 3a}$
3. ${2(b + 3) \over 3a}$
4. ${2(b + 3) \over 3b}$
${2(b + 3) \over 3b}$
• Logarithm manipulation
• Hard
5. ### Logarithm - Inequalities

${log_3{x-3} \over log_3{x-5}}$ < 0. If a, b are integers such that x = a, and x = b satisfy this inequation, find the maximum possible value of a – b.

1. 214
2. 216
3. 200
4. 203
214
• Logarithm - Inequalities
• Hard
6. ### Logarithms - Different bases

log5x = a (This should be read as log X to the base 5 equals a) log20x = b. What is logx10?

1. ${a + b \over 2ab}$
2. (a + b) * 2ab
3. ${2ab \over a + b}$
4. ${a + b \over 2}$
${a + b \over 2ab}$
• Logarithm - Algebra
• Medium
7. ### Basic identities of Logarithm

$Log_{3}x + Log_{x}3 = \frac{17}{4}.$Find x.

1. $3^{4}$
2. $3^{\frac{1}{8}}$
3. $3^{\frac{1}{4}}$
4. $3^{\frac{1}{3}}$
$3^{\frac{1}{4}}$
• Basic identities of Logarithm
• Medium
8. ### Basic identities of Logarithm

$Log_{x}y + Log_{y}x^{2} = 3.$ Find $Log_{x}y^{3}.$

1. 4
2. 3
3. $3^{\frac{1}{2}}$
4. $3^{\frac{1}{16}}$
3
• Basic identities of Logarithm
• Medium
9. ### Basic identities of Logarithm

If log2 4 * log4 8 * log8 16 * ……………nth term = 49, what is the value of n?

1. 49
2. 48
3. 34
4. 24
48
• Basic identities of Logarithm
• Hard
10. ### Basic identities of Logarithm

If 33+6+9+……….x terms = (0.$\overline{037}$)-66 and (x > 70),
What is the value of x?

1. 3
2. 6
3. 7
4. 11
11
• Basic identities of Logarithm
• Hard
11. ### Basic identities of Logarithm

x,y,z are 3 integers in a geometric sequence such that y- x is a perfect cube.
Given, log36x2 + log6√y + 3log216y1/2z = 6. Find the value of x+y+z.

1. 189
2. 190
3. 199
4. 201
189
• Basic identities of Logarithm
• Hard
12. ### Basic identities of Logarithm

10log(3 - 10logy) = log2(9 - 2y), Solve for y

1. 0
2. 3
3. 0 and 3
4. none of these
none of these
• Basic identities of Logarithm
• Medium
13. ### Value of x

46+12+18+24+…+6x = (0.0625)-84, what is the value of x?

1. 7
2. 6
3. 9
4. 12

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