What is the answer to 4^{2x+1}=17(4^x)-15 ?

The answer to 4^{2x+1}=17(4^x)-15 is x=(ln(3))/(2ln(2)),x=(ln(5/4))/(2ln(2))

Solve for x: 4^{2x+1}=17(4^x)-15

The solution is x=(ln(3))/(2ln(2)),x=(ln(5/4))/(2ln(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4^{2 x + 1} = 17 (4^{x}) - 15

x = \frac{ln ( 3 )}{2 ln ( 2 )}, x = \frac{ln ( \frac{5}{4} )}{2 ln ( 2 )}

Solution steps

4^{2 x + 1} = 17 (4^{x}) - 15

Apply exponent rules

(4^{x})^{2} \cdot 4^{1} = 17 \cdot 4^{x} - 15

Rewrite the equation with

4^{x} = u

(u)^{2} \cdot 4^{1} = 17 u - 15

Solve

u^{2} \cdot 4^{1} = 17 u - 15 : u = 3, u = \frac{5}{4}

u = 3, u = \frac{5}{4}

Substitute back

u = 4^{x},

solve for

x

Solve

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

Solve

4^{x} = \frac{5}{4} : x = \frac{ln ( \frac{5}{4} )}{2 ln ( 2 )}

x = \frac{ln ( 3 )}{2 ln ( 2 )}, x = \frac{ln ( \frac{5}{4} )}{2 ln ( 2 )}

2^{x + 2} + 2^{x + 1} + 2^{x} = 896

4^{x + 3} = 8^{3 x - 4}

3^{2 x - 3} = 6

2^{x - 3} = 5

9 (5^{x}) = 8^{x + 4}

What is the answer to 4^{2x+1}=17(4^x)-15 ?
The answer to 4^{2x+1}=17(4^x)-15 is x=(ln(3))/(2ln(2)),x=(ln(5/4))/(2ln(2))
Solve for x: 4^{2x+1}=17(4^x)-15
The solution is x=(ln(3))/(2ln(2)),x=(ln(5/4))/(2ln(2))