What is the answer to 5^x+5^{x+1}+5^{x-2}+5^{x-3}=780 ?

The answer to 5^x+5^{x+1}+5^{x-2}+5^{x-3}=780 is x=(ln(65/63))/(ln(5))+3

Solve for x: 5^x+5^{x+1}+5^{x-2}+5^{x-3}=780

The solution is x=(ln(65/63))/(ln(5))+3

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5^{x} + 5^{x + 1} + 5^{x - 2} + 5^{x - 3} = 780

x = \frac{ln ( \frac{65}{63} )}{ln ( 5 )} + 3

Decimal Notation

x = 3.01941 \dots

Solution steps

5^{x} + 5^{x + 1} + 5^{x - 2} + 5^{x - 3} = 780

Factor

5^{x} + 5^{x + 1} + 5^{x - 2} + 5^{x - 3} : 756 \cdot 5^{x - 3}

756 \cdot 5^{x - 3} = 780

Divide both sides by

756

5^{x - 3} = \frac{65}{63}

Apply exponent rules

(x - 3) ln (5) = ln (\frac{65}{63})

Solve

(x - 3) ln (5) = ln (\frac{65}{63}) : x = \frac{ln ( \frac{65}{63} )}{ln ( 5 )} + 3

x = \frac{ln ( \frac{65}{63} )}{ln ( 5 )} + 3

ln (e^{x + 3}) = 10

3^{x} = \frac{1}{81}

3^{2 x} - 3^{x} - 72 = 0

e^{- 2 k} = 0

2^{3 x} \cdot 7^{x - 1} = 4^{x + 1}

What is the answer to 5^x+5^{x+1}+5^{x-2}+5^{x-3}=780 ?
The answer to 5^x+5^{x+1}+5^{x-2}+5^{x-3}=780 is x=(ln(65/63))/(ln(5))+3
Solve for x: 5^x+5^{x+1}+5^{x-2}+5^{x-3}=780
The solution is x=(ln(65/63))/(ln(5))+3