What is the answer to 3(2^{2x})-13(2^x)+12=0 ?

The answer to 3(2^{2x})-13(2^x)+12=0 is x=(ln(3))/(ln(2)),x=(ln(4/3))/(ln(2))

Solve for x: 3(2^{2x})-13(2^x)+12=0

The solution is x=(ln(3))/(ln(2)),x=(ln(4/3))/(ln(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3 (2^{2 x}) - 13 (2^{x}) + 12 = 0

x = \frac{ln ( 3 )}{ln ( 2 )}, x = \frac{ln ( \frac{4}{3} )}{ln ( 2 )}

Decimal Notation

x = 1.58496 \dots, x = 0.41503 \dots

Solution steps

3 (2^{2 x}) - 13 (2^{x}) + 12 = 0

Apply exponent rules

3 (2^{x})^{2} - 13 \cdot 2^{x} + 12 = 0

Rewrite the equation with

2^{x} = u

3 (u)^{2} - 13 u + 12 = 0

Solve

3 u^{2} - 13 u + 12 = 0 : u = 3, u = \frac{4}{3}

u = 3, u = \frac{4}{3}

Substitute back

u = 2^{x},

solve for

x

Solve

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

Solve

2^{x} = \frac{4}{3} : x = \frac{ln ( \frac{4}{3} )}{ln ( 2 )}

x = \frac{ln ( 3 )}{ln ( 2 )}, x = \frac{ln ( \frac{4}{3} )}{ln ( 2 )}

2^{x + 7} = 256

4^{2 x} - 4^{x + 1} + 3 = 0

x, 1 = y^{2 x - 1}

11 e^{x} = 1

3^{x} = 2^{7}

What is the answer to 3(2^{2x})-13(2^x)+12=0 ?
The answer to 3(2^{2x})-13(2^x)+12=0 is x=(ln(3))/(ln(2)),x=(ln(4/3))/(ln(2))
Solve for x: 3(2^{2x})-13(2^x)+12=0
The solution is x=(ln(3))/(ln(2)),x=(ln(4/3))/(ln(2))