What is the answer to 3^{x+1}-4+1/(3^x)=0 ?

The answer to 3^{x+1}-4+1/(3^x)=0 is x=0,x=-1

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3^{x+1}-4+1/(3^x)=0

3^{x + 1} - 4 + \frac{1}{3 ^{x}} = 0

x = 0, x = - 1

Solution steps

3^{x + 1} - 4 + \frac{1}{3 ^{x}} = 0

Apply exponent rules

3^{x} \cdot 3^{1} - 4 + (3^{x})^{- 1} = 0

Rewrite the equation with

3^{x} = u

u \cdot 3^{1} - 4 + (u)^{- 1} = 0

Solve

u \cdot 3^{1} - 4 + u^{- 1} = 0 : u = 1, u = \frac{1}{3}

u = 1, u = \frac{1}{3}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 1 : x = 0

Solve

3^{x} = \frac{1}{3} : x = - 1

x = 0, x = - 1

Verify Solutions:

x = 0

True

, x = - 1

True

The solutions are

x = 0, x = - 1

1 0^{x} = 22.4

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

6^{4 - x} = \frac{1}{42}

6^{9 - 2 x} = 36

8^{5 x + 5} = 3 2^{2 x - 2}

What is the answer to 3^{x+1}-4+1/(3^x)=0 ?
The answer to 3^{x+1}-4+1/(3^x)=0 is x=0,x=-1
Solve for x: 3^{x+1}-4+1/(3^x)=0
The solution is x=0,x=-1