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ehidna [41]
4 years ago
9

Solve the equation. Round to the nearest hundredth. Show work.

Mathematics
1 answer:
Elis [28]4 years ago
6 0

Answer:

The value of x = 0.41

Step-by-step explanation:

∵ 6e^{2x}-5e^{x}=6

Let e^{x}=y

∴ e^{2x}=y^{2}

∴ 6y² - 5y = 6

∴ 6y² - 5y - 6 = 0 ⇒ factorize

∴ (3y + 2)(2y - 3) = 0

∴ 3y + 2 = 0 ⇒ 3y = -2 ⇒ y = -2/3

∴ 2y - 3 = 0 ⇒ 2y = 3 ⇒ y = 3/2

∵ y=e^{x}

∴ e^{x}=\frac{-2}{3} ⇒ refused

  (e^{ax} never gives -ve values)

∵ e^{x}=3/2 ⇒ insert <em>ln</em> in both sides

∵ lne^{ax}=axlne=ax ⇒ <em>ln</em>(e) <em>= 1</em>

∴ xlne=ln(3/2)

∴ x = ln(3/2) = 0.41

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