What is the answer to 3^{x-1}+3^{x-2}=108 ?

The answer to 3^{x-1}+3^{x-2}=108 is x=5

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3^{x-1}+3^{x-2}=108

3^{x - 1} + 3^{x - 2} = 108

x = 5

Solution steps

3^{x - 1} + 3^{x - 2} = 108

Factor

3^{x - 1} + 3^{x - 2} : 4 \cdot 3^{x - 2}

4 \cdot 3^{x - 2} = 108

Divide both sides by

4

3^{x - 2} = 27

Apply exponent rules

x - 2 = 3

Solve

x - 2 = 3 : x = 5

x = 5

1 0^{x} = 0.0001

2^{2 x} = 8

4 - 2 e^{x} = - 23

2^{x^{2}} = 2

4 \cdot 3^{x - 1} - 1 = 3^{2 x - 1}

What is the answer to 3^{x-1}+3^{x-2}=108 ?
The answer to 3^{x-1}+3^{x-2}=108 is x=5
Solve for x: 3^{x-1}+3^{x-2}=108
The solution is x=5