What is the answer to 3^{x+2}=3^x+1994 ?

The answer to 3^{x+2}=3^x+1994 is x=(ln(997/4))/(ln(3))

Solve for x: 3^{x+2}=3^x+1994

The solution is x=(ln(997/4))/(ln(3))

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3^{x + 2} = 3^{x} + 1994

x = \frac{ln ( \frac{997}{4} )}{ln ( 3 )}

Decimal Notation

x = 5.02311 \dots

Solution steps

3^{x + 2} = 3^{x} + 1994

Subtract

3^{x}

from both sides

3^{x + 2} - 3^{x} = 3^{x} + 1994 - 3^{x}

Simplify

3^{x + 2} - 3^{x} = 1994

Factor

3^{x + 2} - 3^{x} : 8 \cdot 3^{x}

8 \cdot 3^{x} = 1994

Divide both sides by

8

3^{x} = \frac{997}{4}

Apply exponent rules

x ln (3) = ln (\frac{997}{4})

Solve

x ln (3) = ln (\frac{997}{4}) : x = \frac{ln ( \frac{997}{4} )}{ln ( 3 )}

x = \frac{ln ( \frac{997}{4} )}{ln ( 3 )}

5^{2 n - 1} - 2 5^{n - 1} = 100

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

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

e^{2 x} - e^{x} = 0

1 + 7^{1} + 7^{2} + 7^{3} = k^{r}

What is the answer to 3^{x+2}=3^x+1994 ?
The answer to 3^{x+2}=3^x+1994 is x=(ln(997/4))/(ln(3))
Solve for x: 3^{x+2}=3^x+1994
The solution is x=(ln(997/4))/(ln(3))