What is the answer to 1/(3^x+3^x+3^x)=81 ?

The answer to 1/(3^x+3^x+3^x)=81 is x=-5

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1/(3^x+3^x+3^x)=81

\frac{1}{3 ^{x} + 3 ^{x} + 3 ^{x}} = 81

x = - 5

Solution steps

\frac{1}{3 ^{x} + 3 ^{x} + 3 ^{x}} = 81

Multiply both sides by

3^{1 + x}

\frac{1}{3 ^{x} + 3 ^{x} + 3 ^{x}} \cdot 3^{1 + x} = 81 \cdot 3^{1 + x}

Simplify

\frac{3 ^{1 + x}}{3 \cdot 3 ^{x}} = 81 \cdot 3^{1 + x}

Apply exponent rules

1 + x = - 4

Solve

1 + x = - 4 : x = - 5

x = - 5

Verify Solutions:

x = - 5

True

The solution is

x = - 5

6 x e^{x} + 5 e^{x + 2} = 0

3^{2 x - 3} = 5^{4 x + 5}

3^{x} = 5^{x - 1}

27 = 3^{5 x} 9^{x^{2}}

e^{x} e^{2} = \frac{e ^{4}}{e ^{x + 1}}

What is the answer to 1/(3^x+3^x+3^x)=81 ?
The answer to 1/(3^x+3^x+3^x)=81 is x=-5
Solve for x: 1/(3^x+3^x+3^x)=81
The solution is x=-5