What is the answer to 7^x+7^{1-x}=8 ?

The answer to 7^x+7^{1-x}=8 is x=1,x=0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

7^x+7^{1-x}=8

7^{x} + 7^{1 - x} = 8

x = 1, x = 0

Solution steps

7^{x} + 7^{1 - x} = 8

Apply exponent rules

7^{x} + (7^{x})^{- 1} \cdot 7^{1} = 8

Rewrite the equation with

7^{x} = u

u + (u)^{- 1} \cdot 7^{1} = 8

Solve

u + u^{- 1} \cdot 7^{1} = 8 : u = 7, u = 1

u = 7, u = 1

Substitute back

u = 7^{x},

solve for

x

Solve

7^{x} = 7 : x = 1

Solve

7^{x} = 1 : x = 0

x = 1, x = 0

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

25 6^{x} = 128

\frac{4 9 ^{4 x - 1}}{7 ^{x - 6}} = 7^{8 x + 3}

3^{x^{2}} + 18 = 27

3^{2 x - 3} = 729