What is the answer to 3^x+3^{x+2}=81 ?

The answer to 3^x+3^{x+2}=81 is x=(ln(81/10))/(ln(3))

Solve for x: 3^x+3^{x+2}=81

The solution is x=(ln(81/10))/(ln(3))

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3^{x} + 3^{x + 2} = 81

x = \frac{ln ( \frac{81}{10} )}{ln ( 3 )}

Decimal Notation

x = 1.90409 \dots

Solution steps

3^{x} + 3^{x + 2} = 81

Factor

3^{x} + 3^{x + 2} : 10 \cdot 3^{x}

10 \cdot 3^{x} = 81

Divide both sides by

10

3^{x} = \frac{81}{10}

Apply exponent rules

x ln (3) = ln (\frac{81}{10})

Solve

x ln (3) = ln (\frac{81}{10}) : x = \frac{ln ( \frac{81}{10} )}{ln ( 3 )}

x = \frac{ln ( \frac{81}{10} )}{ln ( 3 )}

1 0^{x} = 12

1 0^{x} = 16

2^{3 x + 7} = 32

2 = (1 + \frac{0.1}{52})^{52 t}

8^{x - 5} = 16

What is the answer to 3^x+3^{x+2}=81 ?
The answer to 3^x+3^{x+2}=81 is x=(ln(81/10))/(ln(3))
Solve for x: 3^x+3^{x+2}=81
The solution is x=(ln(81/10))/(ln(3))