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

The answer to 3^{x+2}=3^x+3^2 is x=(ln(9/8))/(ln(3))

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

The solution is x=(ln(9/8))/(ln(3))

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

x = \frac{ln ( \frac{9}{8} )}{ln ( 3 )}

Solution steps

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

Subtract

3^{x}

from both sides

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

Simplify

3^{x + 2} - 3^{x} = 9

Factor

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

8 \cdot 3^{x} = 9

Divide both sides by

8

3^{x} = \frac{9}{8}

Apply exponent rules

x ln (3) = ln (\frac{9}{8})

Solve

x ln (3) = ln (\frac{9}{8}) : x = \frac{ln ( \frac{9}{8} )}{ln ( 3 )}

x = \frac{ln ( \frac{9}{8} )}{ln ( 3 )}

5^{2 x + 1} = 6^{x - 2}

e^{2 l n (x)} = 9

4 \cdot 1 0^{- 3 x} = 18

2^{x - 1} = 16

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

What is the answer to 3^{x+2}=3^x+3^2 ?
The answer to 3^{x+2}=3^x+3^2 is x=(ln(9/8))/(ln(3))
Solve for x: 3^{x+2}=3^x+3^2
The solution is x=(ln(9/8))/(ln(3))