What is the answer to 3^x+3^{x-1}+3^{x-2}=13 ?

The answer to 3^x+3^{x-1}+3^{x-2}=13 is x=2

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3^x+3^{x-1}+3^{x-2}=13

3^{x} + 3^{x - 1} + 3^{x - 2} = 13

x = 2

Solution steps

3^{x} + 3^{x - 1} + 3^{x - 2} = 13

Factor

3^{x} + 3^{x - 1} + 3^{x - 2} : 13 \cdot 3^{x - 2}

13 \cdot 3^{x - 2} = 13

Divide both sides by

13

3^{x - 2} = 1

Apply exponent rules

(x - 2) ln (3) = ln (1)

Solve

(x - 2) ln (3) = ln (1) : x = 2

x = 2

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

1 6^{x} = 8^{2 x + 3}

lo g_{10} (43) = 4. 2^{x}

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

e^{- 8 n - 9} = 36.5

What is the answer to 3^x+3^{x-1}+3^{x-2}=13 ?
The answer to 3^x+3^{x-1}+3^{x-2}=13 is x=2
Solve for x: 3^x+3^{x-1}+3^{x-2}=13
The solution is x=2