What is the answer to 3^{x+3}+1/(3^x)-28=0 ?

The answer to 3^{x+3}+1/(3^x)-28=0 is x=0,x=-3

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3^{x+3}+1/(3^x)-28=0

3^{x + 3} + \frac{1}{3 ^{x}} - 28 = 0

x = 0, x = - 3

Solution steps

3^{x + 3} + \frac{1}{3 ^{x}} - 28 = 0

Apply exponent rules

3^{x} \cdot 3^{3} + (3^{x})^{- 1} - 28 = 0

Rewrite the equation with

3^{x} = u

u \cdot 3^{3} + (u)^{- 1} - 28 = 0

Solve

u \cdot 3^{3} + u^{- 1} - 28 = 0 : u = 1, u = \frac{1}{27}

u = 1, u = \frac{1}{27}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 1 : x = 0

Solve

3^{x} = \frac{1}{27} : x = - 3

x = 0, x = - 3

Verify Solutions:

x = 0

True

, x = - 3

True

The solutions are

x = 0, x = - 3

75 e^{- 0.1 (t)} = 3

20 x + 1 = 3^{x}

(\frac{1}{5})^{x} = 625

5 (2^{2 p + 1}) - 17 (2^{p + 3}) = 0

2048 = 4 \cdot 2^{x}

What is the answer to 3^{x+3}+1/(3^x)-28=0 ?
The answer to 3^{x+3}+1/(3^x)-28=0 is x=0,x=-3
Solve for x: 3^{x+3}+1/(3^x)-28=0
The solution is x=0,x=-3