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Question Number 166633 by mathlove last updated on 23/Feb/22

	Answered by mahdipoor last updated on 23/Feb/22

	$x y z = {l o g}_{2 a} a \times {l o g}_{3 a} 2 a \times {l o g}_{4 a} 3 a =$ $\frac{l n a}{l n 2 a} \times \frac{l n 2 a}{l n 3 a} \times \frac{l n 3 a}{l n 4 a} = \frac{l n a}{l n 4 a}$ $y z = {l o g}_{3 a} 2 a \times {l o g}_{4 a} 3 a = \frac{l n 2 a}{l n 3 a} \times \frac{l n 3 a}{l n 4 a} = \frac{l n 2 a}{l n 4 a}$ $1 + x y z = \frac{l n 4 a + l n a}{l n 4 a} = \frac{l n 4 a^{2}}{l n 4 a} = \frac{2 l n 2 a}{l n 4 a} = 2 y z$
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