What is the answer to 3^{x-1}+3^x+3^{x-1}=26 ?

The answer to 3^{x-1}+3^x+3^{x-1}=26 is x=(ln(26/5))/(ln(3))+1

Solve for x: 3^{x-1}+3^x+3^{x-1}=26

The solution is x=(ln(26/5))/(ln(3))+1

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3^{x - 1} + 3^{x} + 3^{x - 1} = 26

x = \frac{ln ( \frac{26}{5} )}{ln ( 3 )} + 1

Decimal Notation

x = 2.50067 \dots

Solution steps

3^{x - 1} + 3^{x} + 3^{x - 1} = 26

Factor

3^{x - 1} + 3^{x} + 3^{x - 1} : 5 \cdot 3^{x - 1}

5 \cdot 3^{x - 1} = 26

Divide both sides by

5

3^{x - 1} = \frac{26}{5}

Apply exponent rules

(x - 1) ln (3) = ln (\frac{26}{5})

Solve

(x - 1) ln (3) = ln (\frac{26}{5}) : x = \frac{ln ( \frac{26}{5} )}{ln ( 3 )} + 1

x = \frac{ln ( \frac{26}{5} )}{ln ( 3 )} + 1

3^{5 x} = 81

10 0^{x} = 100

3 (2^{(x)} + 1) - 2^{(x + 2)} + 5 = 0

3^{x - 4} = 1

2^{x - 5} = 3^{4 x + 1}

What is the answer to 3^{x-1}+3^x+3^{x-1}=26 ?
The answer to 3^{x-1}+3^x+3^{x-1}=26 is x=(ln(26/5))/(ln(3))+1
Solve for x: 3^{x-1}+3^x+3^{x-1}=26
The solution is x=(ln(26/5))/(ln(3))+1