Solve the following equation for x: log 4 32 = x - 4

Given, ⇒ log 4 32 = x - 4 ⇒ 4 x - 4 = 32 ⇒ (2 2 ) x - 4 = 2 5 ⇒ 2 2x - 8 = 2 5 ⇒ 2x - 8 = 5 ⇒ 2x = 13 ⇒ x = . Hence, x = .

Mathematics

22 Likes

Given,

⇒ log₄ 32 = x - 4

⇒ 4^{x - 4} = 32

⇒ (2²)^{x - 4} = 2⁵

⇒ 2^{2x - 8} = 2⁵

⇒ 2x - 8 = 5

⇒ 2x = 13

⇒ x = $\dfrac{13}{2} = 6\dfrac{1}{2}$ .

Hence, x = $6\dfrac{1}{2}$ .

Answered By

7 Likes