What is the answer to 8^x+8^{x-1}+8^{x+1}=292 ?

The answer to 8^x+8^{x-1}+8^{x+1}=292 is x= 5/3

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8^x+8^{x-1}+8^{x+1}=292

8^{x} + 8^{x - 1} + 8^{x + 1} = 292

x = \frac{5}{3}

Decimal Notation

x = 1.66666 \dots

Solution steps

8^{x} + 8^{x - 1} + 8^{x + 1} = 292

Factor

8^{x} + 8^{x - 1} + 8^{x + 1} : 73 \cdot 8^{x - 1}

73 \cdot 8^{x - 1} = 292

Divide both sides by

73

8^{x - 1} = 4

Apply exponent rules

3 (x - 1) = 2

Solve

3 (x - 1) = 2 : x = \frac{5}{3}

x = \frac{5}{3}

(n - 2)^{(n - 2) 2} = 2

2 x^{4} e^{- 2 x} = 0

4^{x + 3} = 64

1.7 \cdot 6^{- 1.7 v} - 6 = 8

3^{x} = \frac{1}{243}

What is the answer to 8^x+8^{x-1}+8^{x+1}=292 ?
The answer to 8^x+8^{x-1}+8^{x+1}=292 is x= 5/3
Solve for x: 8^x+8^{x-1}+8^{x+1}=292
The solution is x= 5/3