What is the answer to 5e^{x^2-6x-9}=1 ?

The answer to 5e^{x^2-6x-9}=1 is x=(6+sqrt(-4ln(5)+72))/2 ,x=(6-sqrt(-4ln(5)+72))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

5e^{x^2-6x-9}=1

5 e^{x^{2} - 6 x - 9} = 1

x = \frac{6 + - 4 ln ( 5 ) + 72}{2}, x = \frac{6 - - 4 ln ( 5 ) + 72}{2}

Decimal Notation

x = 7.04852 \dots, x = - 1.04852 \dots

Solution steps

5 e^{x^{2} - 6 x - 9} = 1

Divide both sides by

5

e^{x^{2} - 6 x - 9} = \frac{1}{5}

Apply exponent rules

x^{2} - 6 x - 9 = ln (\frac{1}{5})

Solve

x^{2} - 6 x - 9 = ln (\frac{1}{5}) : x = \frac{6 + - 4 ln ( 5 ) + 72}{2}, x = \frac{6 - - 4 ln ( 5 ) + 72}{2}

x = \frac{6 + - 4 ln ( 5 ) + 72}{2}, x = \frac{6 - - 4 ln ( 5 ) + 72}{2}

15 = 12 e^{x - 2}

3^{x + 2} = 2^{1 - x}

e^{x} = x^{10}

e^{2 x} = 18

(e^{4})^{x} (e^{x})^{2} = e^{12}

What is the answer to 5e^{x^2-6x-9}=1 ?
The answer to 5e^{x^2-6x-9}=1 is x=(6+sqrt(-4ln(5)+72))/2 ,x=(6-sqrt(-4ln(5)+72))/2