Question

find the value of x if 2powerx + 1 equal to3 power 1 - x​

Answer 1

Answer:

x = ( log 3/2 ) / ( log 6 )

Explanation:

Given,

2ˣ ⁺ ¹ = 3¹ ⁻ ˣ

Taking log on both sides

⇒ log2ˣ ⁺ ¹ = log3¹ ⁻ ˣ

Using Power rule loga^m = m.loga we get

⇒ ( x + 1 ) log 2 = ( 1 - x ) log 3

⇒ xlog 2 + log 2 = log 3 - x log 3

⇒ xlog 2 + x log 3 = log 3 - log 2

Taking x common in LHS

⇒ x ( log 2 + log 3 ) = log 3 - log 2

Using Product rule log a + log b = log ab we get,

⇒ x ( log 2 × 3 ) = log 3 - log 2

⇒ x ( log 6 ) = log 3 - log 2

Using Quotient rule log a - log b = log a / b we get,

⇒ x ( log 6 ) = log 3/2

⇒ x = ( log 3/2 ) / ( log 6 )

Therefore we get the value of x.