What is the answer to (100)/(e^{2x)}=(300)/(e^{4x)} ?

The answer to (100)/(e^{2x)}=(300)/(e^{4x)} is x=(ln(3))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(100)/(e^{2x)}=(300)/(e^{4x)}

\frac{100}{e ^{2 x}} = \frac{300}{e ^{4 x}}

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

Decimal Notation

x = 0.54930 \dots

Solution steps

\frac{100}{e ^{2 x}} = \frac{300}{e ^{4 x}}

Apply exponent rules

ln (100) - 2 x = ln (300) - 4 x

Solve

ln (100) - 2 x = ln (300) - 4 x : x = \frac{ln ( 3 )}{2}

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

Verify Solutions:

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

True

The solution is

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

5^{2 x} - 2 \times 5^{x} - 15 = 0

5^{x + 3} = 125

7^{x} = 343

e^{2 x} - 2 e^{x} - 8 = 0

2^{2 x} = 2^{43}

What is the answer to (100)/(e^{2x)}=(300)/(e^{4x)} ?
The answer to (100)/(e^{2x)}=(300)/(e^{4x)} is x=(ln(3))/2