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Popular >

e^{2x}-5e^x=24

Solution

e^{2 x} - 5 e^{x} = 24

Solution

x = 3 ln (2)

+1

Decimal Notation

x = 2.07944 \dots

Solution steps

e^{2 x} - 5 e^{x} = 24

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

(u)^{2} - 5 u = 24

Solve

u^{2} - 5 u = 24 : u = 8, u = - 3

u = 8, u = - 3

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 8 : x = 3 ln (2)

Solve

e^{x} = - 3 :

No Solution for

x \in R

x = 3 ln (2)

Popular Examples

e^{x/(200)}+2e^{-x/(200)}=4

e^{\frac{x}{200}} + 2 e^{- \frac{x}{200}} = 4

6^{x + 1} = 1 3^{x}

5^{x+1}+5^x+5^{x-1}=31

5^{x + 1} + 5^{x} + 5^{x - 1} = 31

2^{x+2}+5\times 2^{x-1}= 13/16

2^{x + 2} + 5 \times 2^{x - 1} = \frac{13}{16}

4e^{3-x}=3^{2x+5}

4 e^{3 - x} = 3^{2 x + 5}

Frequently Asked Questions (FAQ)

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