WBBSE Class 9 Maths Algebra Chapter 6 Logarithm Multiple Choice Questions

WBBSE Class 9 Maths Algebra Chapter 6 Logarithm Multiple Choice Questions

Example 1. If log_√x0.25 = 4 then the value of x

1. 0.5
2. 0.25
3. 4
4. 16

Solution: The correct answer is 1. 0.5

⇒ (√x)⁴ = 0·25

⇒ \(x^{\frac{1}{2} \times 4}=(0 \cdot 5)^2\)

∴ x = 0.5

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The value of x = 0.5

Example 2. If log₁₀(7x – 5) = 2, then the value of x

1. 10
2. 12
3. 15
4. 18

Solution: The correct answer is 3. 15

⇒ 10² = 7x – 5

⇒ or, 7x = 100+ 5

⇒ or, x = 15

The value of x = 15

Example 3. If log₂³ = a, then log₈²⁷ =?

1. 3a
2. \(\frac{1}{a}\)
3. 2a
4. a

Solution: The correct answer is 4. a

⇒ \(\log _8 27=\frac{\log _2 27}{\log _2 8}\)

= \(\frac{3 \log _2 3}{3 \log _2 2}=\frac{a}{1}=a\)

log₈²⁷ = \(\frac{3 \log _2 3}{3 \log _2 2}=\frac{a}{1}=a\)

Example 4. If logx_√2 = a then, the value of logx_2√2 is

1. \(\frac{a}{3}\)
2. a
3. 2a
4. 3a

Solution: The correct answer is 1. \(\frac{a}{3}\)

⇒ x = (√2)^a

⇒ or, \(\log _{2 \sqrt{2}} x=\log _{2 \sqrt{2}}(\sqrt{2})^a=a \log _{2 \sqrt{2}} \sqrt{2}\)

= \(a \frac{\log _b \sqrt{2}}{\log _b 2 \sqrt{2}}(b \neq 0,1)=a \frac{\log _b(2)^{\frac{1}{2}}}{\log _b(2)^{\frac{3}{2}}}\)

= \(a \cdot \frac{\frac{1}{2} \log _b 2}{\frac{3}{2} \log _b 2}=\frac{a}{3}\)

The value of logx_2√2 = \(a \cdot \frac{\frac{1}{2} \log _b 2}{\frac{3}{2} \log _b 2}=\frac{a}{3}\)

Example 5. If \(\log _x \frac{1}{3}=-\frac{1}{3}\) then the value of x is

1. 27
2. 9
3. 3
4. \(\frac{1}{27}\)

Solution: The correct answer is 1. 27

⇒ \((x)^{-\frac{1}{3}}=\frac{1}{3}\)

⇒ or, \(x=\left(\frac{1}{3}\right)^{-3}=3^3=27\)

The value of x is \(x=\left(\frac{1}{3}\right)^{-3}=3^3=27\)

Example 6. \(\log _3\left(\frac{1}{81}\right)=?\)

1. -1
2. -2
3. -3
4. -4

Solution: The correct answer is 1. -1

⇒ Let \(\log _3\left(\frac{1}{81}\right)=x\)

∴ 3^x = 3^-4, x = -4

Example 7. If log_√7 = x then the value of x is

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

Solution: The correct answer is 2. 6

⇒ (√7)^x = 243 =7³

⇒ or, \(7^{\frac{x}{2}}=7^3\)

⇒ x = 6

The value of x is 6.

Example 8. State which of the following is the value of log_0.008√5

1. –\(\frac{1}{6}\)
2. –\(\frac{1}{3}\)
3. –\(\frac{1}{2}\)
4. –\(\frac{1}{8}\)

Solution: The correct answer is 1. –\(\frac{1}{6}\)

⇒ Let _0.008√5 = x

⇒ \((008)^x=\sqrt{5}\)

⇒ or, \(5^{-3 x}=5^{\frac{1}{2}} \quad x=-\frac{1}{6}\)

The value of log_0.008√5 \(5^{-3 x}=5^{\frac{1}{2}} \quad x=-\frac{1}{6}\)

Example 9. \(\log _4 2^{-8}=\)?

1. – 4
2. – 3
3. – 2
4. – 1

Solution: The correct answer is 1. -4

⇒ Let \(\log _4 2^{-8}=x\)

∴ \(4^x=2^{-8}\)

⇒ or, 2x = -8, x = -4

Example 10. If the logarithm of 5832 be 6, then the base is

1. 2√3
2. 3
3. 2
4. 3√2

Solution: The correct answer is 4. 3√2

⇒ Let log_x5832 = 6

⇒ x⁶ = 5832 = 3⁶, 2³

⇒ or, x⁶ =(3√2)⁶,

⇒ x = 3√2

The base is x = 3√2