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Solve the following equation: a) e^4x + 4e^2x - 21 = 0 b) log base 2 (log base 3 x) = 4

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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a) `e^(4x) + 4e^(2x) - 12 = 0 `

`==gt (e^(2x))^2 + 4e^(2x) - 12 = 0`

Let `e^(2x)= u `

`==> u^2 + 4u -12 = 0`

Now we will factor.

`==gt (u+6)(u-2) = 0 `

`==gt u= -6 ==gt e^(2x)= -6 ==gtx= phi`

`==gt u= 2 ==gt e^(2x) = 2==gt 2x = ln 2==gt x = ln2/2 ~~0.35`

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b) `log_2 (log_3 x) = 4`

`==> log_3 x = 2^4`

`=> log_3 x = 16`

`==> x = 3^16 `

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