What is the answer to 7*7^x+1/(7^x)=8 ?

The answer to 7*7^x+1/(7^x)=8 is x=0,x=-1

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7*7^x+1/(7^x)=8

7 \cdot 7^{x} + \frac{1}{7 ^{x}} = 8

x = 0, x = - 1

Solution steps

7 \cdot 7^{x} + \frac{1}{7 ^{x}} = 8

Apply exponent rules

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

Rewrite the equation with

7^{x} = u

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

Solve

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

u = 1, u = \frac{1}{7}

Substitute back

u = 7^{x},

solve for

x

Solve

7^{x} = 1 : x = 0

Solve

7^{x} = \frac{1}{7} : x = - 1

x = 0, x = - 1

Verify Solutions:

x = 0

True

, x = - 1

True

The solutions are

x = 0, x = - 1

2^{x + 1} \cdot 4^{x + 2} = 8

9^{8 - 3 x} = (3^{2})^{2 x - 2}

e^{3 k} = 5

e^{4 x} = 6

8^{- x} = 2

What is the answer to 7*7^x+1/(7^x)=8 ?
The answer to 7*7^x+1/(7^x)=8 is x=0,x=-1
Solve for x: 7*7^x+1/(7^x)=8
The solution is x=0,x=-1