en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

e^{4x}+5e^{2x}-24=0

Solution

e^{4 x} + 5 e^{2 x} - 24 = 0

Solution

x = \frac{1}{2} ln (3)

+1

Decimal Notation

x = 0.54930 \dots

Solution steps

e^{4 x} + 5 e^{2 x} - 24 = 0

Apply exponent rules

(e^{x})^{4} + 5 (e^{x})^{2} - 24 = 0

Rewrite the equation with

e^{x} = u

(u)^{4} + 5 (u)^{2} - 24 = 0

Solve

u^{4} + 5 u^{2} - 24 = 0 : u = 3, u = - 3

u = 3, u = - 3

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 3 : x = \frac{1}{2} ln (3)

Solve

e^{x} = - 3 :

No Solution for

x \in R

x = \frac{1}{2} ln (3)

Popular Examples

(1/2)^x=\sqrt[3]{4}

8^{x+1}*2^{2x}=4^{3x-1}

8^{x + 1} \cdot 2^{2 x} = 4^{3 x - 1}

3^{7-2x}=(1/27)^{-8}

3^{7 - 2 x} = (\frac{1}{27})^{- 8}

73 = 2 3^{x}

9^{x+1}+3=28*3^x

9^{x + 1} + 3 = 28 \cdot 3^{x}

Frequently Asked Questions (FAQ)

What is the answer to e^{4x}+5e^{2x}-24=0 ?
The answer to e^{4x}+5e^{2x}-24=0 is x= 1/2 ln(3)