Assertion (A): If log10x log105 = log1020 ⇒ 5x = 20 and x = 4 Reason (R): If log10x log105 = log1020 ⇒ x + 5 = 20 and x = 15 1. A is true, R is false. 2. A is false, R is true. 3. Both A and R are true. 4. Both A and R are false.

Both A and R are false. Explanation Given, log10x log105 = log1020 Let log10x = a. Then, ⇒ a. log105 = log1020 ⇒ a = Using the property lognm = ⇒ a = log520 ⇒ log10x = log520 Using the logarithmic identity logba = c ⇒ bc = a, ⇒ x = 5log520 = 20 ∴ x ≠ 4 ∴ Assertion (A) is false. It is shown above, log10x log105 = log1020 ⇒ x = 20 ∴ x ≠ 15 ∴ Reason (R) is false. Hence, both Assertion (A) and Reason (R) are false.

Mathematics

Assertion (A): If log₁₀x $\times$ log₁₀5 = log₁₀20
⇒ 5x = 20 and x = 4
Reason (R): If log₁₀x $\times$ log₁₀5 = log₁₀20
⇒ x + 5 = 20 and x = 15
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.

Logarithms

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Answer

Both A and R are false.

Explanation

Given,

log₁₀x $\times$ log₁₀5 = log₁₀20

Let log₁₀x = a.

Then,

⇒ a. log₁₀5 = log₁₀20

⇒ a = $\dfrac{log$

Using the property log_nm = $\dfrac{log$

⇒ a = log₅20

⇒ log₁₀x = log₅20

Using the logarithmic identity log_ba = c ⇒ b^c = a,

⇒ x = 5^log₅20 = 20

∴ x ≠ 4

∴ Assertion (A) is false.

It is shown above, log₁₀x $\times$ log₁₀5 = log₁₀20 ⇒ x = 20

∴ x ≠ 15

∴ Reason (R) is false.

Hence, both Assertion (A) and Reason (R) are false.

Answered By

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Mathematics

Assertion (A): If log₁₀x $\times$ log₁₀5 = log₁₀20
⇒ 5x = 20 and x = 4
Reason (R): If log₁₀x $\times$ log₁₀5 = log₁₀20
⇒ x + 5 = 20 and x = 15
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.

Logarithms

Answer

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Assertion (A): If log10x ×\times× log105 = log1020⇒ 5x = 20 and x = 4Reason (R): If log10x ×\times× log105 = log1020⇒ x + 5 = 20 and x = 15A is true, R is false.A is false, R is true.Both A and R are true.Both A and R are false.

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