Wisk. Mult. Choice Vraag uit Gricha's Wiskundige Vragenbank

Welk getal is gelijk aan $3^{\log_5\: 7}$ ?	A. $7^{\log_3\:5}$
	B. $7^{\log_5\:3}$
	C. $3^{\log_7\:5}$
	D. $5^{\log_3\:7}$
	E. $5^{\log_7\:3}$

[ 6-6281 - op net sinds 5.12.11-(E)-3.12.2023 ]

Translation in E N G L I S H

Which number is equal to $3^{\log_5\: 7}$ ?	A. $7^{\log_3\: 5}$
	B. $7^{\log_5\: 3}$
	C. $3^{\log_7\: 5}$
	D. $5^{\log_3\: 7}$
	E. $5^{\log_7\: 3}$

Oplossing - Solution

>x₁ = x₂ ⇔ log₅ x₁ = log₅ x₂ (x₁, x₂ > 0)
3^log₅ 7 = 7^log₅ 3
⇔ log₅ 3^log₅ 7 = log₅ 7^log₅ 3
⇔ log₅ 7 . log₅ 3 = log₅ 3 . log₅ 7
→ ! EVIDENT !