What is the answer to 9^x+9^{x+1}=270 ?

The answer to 9^x+9^{x+1}=270 is x= 3/2

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9^x+9^{x+1}=270

9^{x} + 9^{x + 1} = 270

x = \frac{3}{2}

Solution steps

9^{x} + 9^{x + 1} = 270

Factor

9^{x} + 9^{x + 1} : 10 \cdot 9^{x}

10 \cdot 9^{x} = 270

Divide both sides by

10

9^{x} = 27

Apply exponent rules

2 x = 3

Solve

2 x = 3 : x = \frac{3}{2}

x = \frac{3}{2}

5^{x + 1} = 125

3^{x} + 3^{x} = 27

e^{- x} = 5

ln (e^{x}) = 4

6 4^{- 2 x + 3} = 1