What is the answer to 5^{x-2}+5^x+5^{x+1}=30 ?

The answer to 5^{x-2}+5^x+5^{x+1}=30 is x=(ln(30/151))/(ln(5))+2

Solve for x: 5^{x-2}+5^x+5^{x+1}=30

The solution is x=(ln(30/151))/(ln(5))+2

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5^{x - 2} + 5^{x} + 5^{x + 1} = 30

x = \frac{ln ( \frac{30}{151} )}{ln ( 5 )} + 2

Decimal

x = 0.99587 \dots

Solution steps

5^{x - 2} + 5^{x} + 5^{x + 1} = 30

Factor

5^{x - 2} + 5^{x} + 5^{x + 1} : 151 \cdot 5^{x - 2}

151 \cdot 5^{x - 2} = 30

Divide both sides by

151

5^{x - 2} = \frac{30}{151}

Apply exponent rules

(x - 2) ln (5) = ln (\frac{30}{151})

Solve

(x - 2) ln (5) = ln (\frac{30}{151}) : x = \frac{ln ( \frac{30}{151} )}{ln ( 5 )} + 2

x = \frac{ln ( \frac{30}{151} )}{ln ( 5 )} + 2

2 5^{x} - 1 5^{x} = 9^{x}

y, x = e^{3 y}

5^{x} + 8 = 26

2400 (1 - e^{3 x}) = 2000

0 = 2 e^{2 x} - 3 e^{1 - 3 x}

What is the answer to 5^{x-2}+5^x+5^{x+1}=30 ?
The answer to 5^{x-2}+5^x+5^{x+1}=30 is x=(ln(30/151))/(ln(5))+2
Solve for x: 5^{x-2}+5^x+5^{x+1}=30
The solution is x=(ln(30/151))/(ln(5))+2