Logarithms Test

Result

Logarithms Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

Find the value of x which satisfies the relation log₁₀2 + log₁₀ (4x + 1) = log₁₀(x + 1) + 1

A
4

B
-4

C
1/4

D
not defined

Solution

log₁₀2 + log₁₀(4x + 1) = log₁₀(x + 1) + 1 ⇔ log₁₀2 + log₁₀(4x + 1) = log₁₀(x + 1) + log₁₀10

⇔ log₁₀[2(4x + 1)] = log₁₀[10(x + 1)] ⇔ 2(4x + 1) = 10(x + 1) ⇔ 10x + 2 = 8x + 10 ⇔ 2x = −8 ⇔ x= −4 When it is putting x = −4than log (x + 1) is not defined
Question 2
1 / -0

Which of the following statements is correct?

A
log₁₀10 = 0

B
log (2 − 3) = log (2 × 3)

C
log₁₀1 = 1

D
log (1 × 2 × 3) = log1 + log2 + log3
Question 3
1 / -0

log 160 is equal to:

A
2 log 2 + 3 log 3

B
3 log 2 + 2 log 3

C
3 log 2 + 2 log 3 − log 5

D
5 log 2 + log 5

Solution

160 = 2 × 2 × 2 × 2 × 2 × 5 So, log160 = log(2⁵ × 5) = log2⁵ + log5 5log2 + log5