What is the answer to 3^x+3^{1-x}=17 ?

The answer to 3^x+3^{1-x}=17 is x=(ln((17+sqrt(277))/2))/(ln(3)),x=(ln((17-sqrt(277))/2))/(ln(3))

Solve for x: 3^x+3^{1-x}=17

The solution is x=(ln((17+sqrt(277))/2))/(ln(3)),x=(ln((17-sqrt(277))/2))/(ln(3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3^{x} + 3^{1 - x} = 17

x = \frac{ln ( \frac{17 + 277}{2} )}{ln ( 3 )}, x = \frac{ln ( \frac{17 - 277}{2} )}{ln ( 3 )}

Decimal Notation

x = 2.56930 \dots, x = - 1.56930 \dots

Solution steps

3^{x} + 3^{1 - x} = 17

Apply exponent rules

3^{x} + (3^{x})^{- 1} \cdot 3^{1} = 17

Rewrite the equation with

3^{x} = u

u + (u)^{- 1} \cdot 3^{1} = 17

Solve

u + u^{- 1} \cdot 3^{1} = 17 : u = \frac{17 + 277}{2}, u = \frac{17 - 277}{2}

u = \frac{17 + 277}{2}, u = \frac{17 - 277}{2}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = \frac{17 + 277}{2} : x = \frac{ln ( \frac{17 + 277}{2} )}{ln ( 3 )}

Solve

3^{x} = \frac{17 - 277}{2} : x = \frac{ln ( \frac{17 - 277}{2} )}{ln ( 3 )}

x = \frac{ln ( \frac{17 + 277}{2} )}{ln ( 3 )}, x = \frac{ln ( \frac{17 - 277}{2} )}{ln ( 3 )}

ln (e^{2 x - 1}) = 5

x, (t^{2})^{x} = t^{8}

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

7^{1 - x} = 4^{3 x + 1}

e^{x} - 1 = 2 - 2 e^{- x}

What is the answer to 3^x+3^{1-x}=17 ?
The answer to 3^x+3^{1-x}=17 is x=(ln((17+sqrt(277))/2))/(ln(3)),x=(ln((17-sqrt(277))/2))/(ln(3))
Solve for x: 3^x+3^{1-x}=17
The solution is x=(ln((17+sqrt(277))/2))/(ln(3)),x=(ln((17-sqrt(277))/2))/(ln(3))