What is the answer to 8^x+1/(8^x)=9 ?

The answer to 8^x+1/(8^x)=9 is x=(ln((9+sqrt(77))/2))/(3ln(2)),x=(ln((9-sqrt(77))/2))/(3ln(2))

Solve for x: 8^x+1/(8^x)=9

The solution is x=(ln((9+sqrt(77))/2))/(3ln(2)),x=(ln((9-sqrt(77))/2))/(3ln(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

8^{x} + \frac{1}{8 ^{x}} = 9

x = \frac{ln ( \frac{9 + 77}{2} )}{3 ln ( 2 )}, x = \frac{ln ( \frac{9 - 77}{2} )}{3 ln ( 2 )}

Decimal Notation

x = 1.05059 \dots, x = - 1.05059 \dots

Solution steps

8^{x} + \frac{1}{8 ^{x}} = 9

Apply exponent rules

8^{x} + (8^{x})^{- 1} = 9

Rewrite the equation with

8^{x} = u

u + (u)^{- 1} = 9

Solve

u + u^{- 1} = 9 : u = \frac{9 + 77}{2}, u = \frac{9 - 77}{2}

u = \frac{9 + 77}{2}, u = \frac{9 - 77}{2}

Substitute back

u = 8^{x},

solve for

x

Solve

8^{x} = \frac{9 + 77}{2} : x = \frac{ln ( \frac{9 + 77}{2} )}{3 ln ( 2 )}

Solve

8^{x} = \frac{9 - 77}{2} : x = \frac{ln ( \frac{9 - 77}{2} )}{3 ln ( 2 )}

x = \frac{ln ( \frac{9 + 77}{2} )}{3 ln ( 2 )}, x = \frac{ln ( \frac{9 - 77}{2} )}{3 ln ( 2 )}

Verify Solutions:

x = \frac{ln ( \frac{9 + 77}{2} )}{3 ln ( 2 )}

True

, x = \frac{ln ( \frac{9 - 77}{2} )}{3 ln ( 2 )}

True

The solutions are

x = \frac{ln ( \frac{9 + 77}{2} )}{3 ln ( 2 )}, x = \frac{ln ( \frac{9 - 77}{2} )}{3 ln ( 2 )}

7^{2 + x} = 98

2^{x^{3}} = 12 8^{x}

4 e^{2 x} + 3 e^{x} = 1

6^{2 x - 1} + 180 = 6^{2 x}

3^{x + 2} = 3^{2 x - 5}

What is the answer to 8^x+1/(8^x)=9 ?
The answer to 8^x+1/(8^x)=9 is x=(ln((9+sqrt(77))/2))/(3ln(2)),x=(ln((9-sqrt(77))/2))/(3ln(2))
Solve for x: 8^x+1/(8^x)=9
The solution is x=(ln((9+sqrt(77))/2))/(3ln(2)),x=(ln((9-sqrt(77))/2))/(3ln(2))