यदि 5^x^-1= (2.5)^log₁₀⁵ है, तो x का मान क्या है?

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CDS 02/2021: Maths Previous Paper (Held On 14 Nov 2021)

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Answer 1

दिया गया है:

5x-1 = (2.5)log105

प्रयुक्त सूत्र:

यदि a^x = n है, तो x = log_aⁿ

log_a^b = log_e^b/log_e^a

गणना:

हमारे पास है, 5x-1 = (2.5)log105

⇒ (2.5)log105 = 5x-1

⇒ log₁₀⁵ = log_2.5^5x-1

⇒ log105 = (x - 1) log2.55

⇒ (x - 1) = (log105)/(log2.55)

⇒ (x - 1) = log₁₀^2.5

⇒ x = log102.5_{+ 1}

⇒ x = log102.5 ₊log₁₀¹⁰

⇒ x = log1010 × 2.5

⇒ x = log1025

⇒ x = log105²

⇒ x = 2log105

∴ x का मान 2log105 है।

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