What is the answer to 5^x+5^{x-1}+5^{x-3}+5^{x-4}=455 ?

The answer to 5^x+5^{x-1}+5^{x-3}+5^{x-4}=455 is x=(ln(65/108))/(ln(5))+4

Solve for x: 5^x+5^{x-1}+5^{x-3}+5^{x-4}=455

The solution is x=(ln(65/108))/(ln(5))+4

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5^{x} + 5^{x - 1} + 5^{x - 3} + 5^{x - 4} = 455

x = \frac{ln ( \frac{65}{108} )}{ln ( 5 )} + 4

Decimal Notation

x = 3.68452 \dots

Solution steps

5^{x} + 5^{x - 1} + 5^{x - 3} + 5^{x - 4} = 455

Factor

5^{x} + 5^{x - 1} + 5^{x - 3} + 5^{x - 4} : 756 \cdot 5^{x - 4}

756 \cdot 5^{x - 4} = 455

Divide both sides by

756

5^{x - 4} = \frac{65}{108}

Apply exponent rules

(x - 4) ln (5) = ln (\frac{65}{108})

Solve

(x - 4) ln (5) = ln (\frac{65}{108}) : x = \frac{ln ( \frac{65}{108} )}{ln ( 5 )} + 4

x = \frac{ln ( \frac{65}{108} )}{ln ( 5 )} + 4

2 5^{x - 3} = 5125

x e^{x} + 1 = 0

4^{- x + 15} = 8^{x}

2^{x + 1} = 4^{x}

3 e^{3 x} = 0

What is the answer to 5^x+5^{x-1}+5^{x-3}+5^{x-4}=455 ?
The answer to 5^x+5^{x-1}+5^{x-3}+5^{x-4}=455 is x=(ln(65/108))/(ln(5))+4
Solve for x: 5^x+5^{x-1}+5^{x-3}+5^{x-4}=455
The solution is x=(ln(65/108))/(ln(5))+4