The intersection of any two disjoint sets If \( (2)^{x+1}=(3)^{1-x} \)

1.	The intersection of any two disjoint sets If \( (2)^{x+1}=(3)^{1-x} \), find the value of \( x \)
Answer» 2^{x + 1} = 3 ^{1 - x} ⇒ 2^x. 2 = 3.3^-x ⇒ 2^x . 3^x = 3/2 (On multiplying both sides by 3^x) ⇒ 6^x = 3/2 (\(\because\) a^xb^x = ab^x) ⇒ x = log₆3/2 ⇒ x = \(\frac{log 3-log 2}{log 6}\) = \(\frac{0.4771-0.3010}{0.778}\) = \(\frac{0.1761}{0.778}\) = 0.226

The intersection of any two disjoint sets If \( (2)^{x+1}=(3)^{1-x} \), find the value of \( x \)

Answer»

2^{x + 1} = 3 ^{1 - x}

⇒ 2^x. 2 = 3.3^-x

⇒ 2^x . 3^x = 3/2 (On multiplying both sides by 3^x)

⇒ 6^x = 3/2 (\(\because\) a^xb^x = ab^x)

⇒ x = log₆3/2

⇒ x = \(\frac{log 3-log 2}{log 6}\) = \(\frac{0.4771-0.3010}{0.778}\)

= \(\frac{0.1761}{0.778}\) = 0.226

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The intersection of any two disjoint sets If \( (2)^{x+1}=(3)^{1-x} \), find the value of \( x \)

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