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MGA20078
26.11.2019 •
Mathematics
Solve the equation. round to the nearest hundredth. show work.
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Ответ:
The value of x = -0.46
Step-by-step explanation:
∵
÷ ![e^{-x}](/tpl/images/0391/6791/7015f.png)
∴![\frac{4e^{5x}}{e^{-x}}-\frac{e^{-x}}{e^{-x}}=\frac{-3e^{2x}}{e^{-x}}](/tpl/images/0391/6791/cf3ea.png)
* Subtract the power of the same bases
∴![4e^{6x}-1=-3e^{3x}](/tpl/images/0391/6791/a76f5.png)
* Let![e^{3x}=y](/tpl/images/0391/6791/cd6ac.png)
∴![e^{6x}=y^{2}](/tpl/images/0391/6791/84fab.png)
∴ 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=e^{3x}](/tpl/images/0391/6791/85cf7.png)
∴ 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
Ответ: