Solve the equation. round to the nearest hundredth. show work.

The value of x = -0.46

Step-by-step explanation:

∵ ÷

∴

* Subtract the power of the same bases

∴

* Let

∴

∴ 4y² - 1 = -3y

∴ 4y² + 3y - 1 = 0 ⇒ factorize

∴ (4y - 1)(y + 1) = 0

∴ y + 1 = 0 ⇒ y = -1

∴ 4y - 1 = 0 ⇒ 4y = 1 ⇒ y = 1/4

∵

∴ y = -1 refused (never gives -ve value)

∴ ⇒ insert ln in both sides

∵ ⇒ ln(e) = 1

∴ 3xln(e) = ln(1/4)

∴ 3x = ln(1/4)

∴ x = [ln(1/4)] ÷ 3 = -0.46