What is the answer to 5^{x+1}+5+5^{x-1}= 31/5 ?

The answer to 5^{x+1}+5+5^{x-1}= 31/5 is x=(ln(3/13))/(ln(5))

Solve for x: 5^{x+1}+5+5^{x-1}= 31/5

The solution is x=(ln(3/13))/(ln(5))

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5^{x + 1} + 5 + 5^{x - 1} = \frac{31}{5}

x = \frac{ln ( \frac{3}{13} )}{ln ( 5 )}

Decimal Notation

x = - 0.91108 \dots

Solution steps

5^{x + 1} + 5 + 5^{x - 1} = \frac{31}{5}

Factor

5^{x + 1} + 5 + 5^{x - 1} : \frac{1}{5} (26 \cdot 5^{x} + 25)

\frac{1}{5} (26 \cdot 5^{x} + 25) = \frac{31}{5}

Multiply both sides by

5

26 \cdot 5^{x} + 25 = 31

Move

25

to the right side

26 \cdot 5^{x} = 6

Divide both sides by

26

5^{x} = \frac{3}{13}

Apply exponent rules

x ln (5) = ln (\frac{3}{13})

Solve

x ln (5) = ln (\frac{3}{13}) : x = \frac{ln ( \frac{3}{13} )}{ln ( 5 )}

x = \frac{ln ( \frac{3}{13} )}{ln ( 5 )}

\frac{6 ^{x} - 7 ( 6 ^{- x} )}{2} = 3

5^{x} = 2 5^{10 x - 8}

2^{x^{2} + 7 x} = 8^{- 4}

x, 2 = e^{x y}

x, ln (e^{x} - 3) = 2

What is the answer to 5^{x+1}+5+5^{x-1}= 31/5 ?
The answer to 5^{x+1}+5+5^{x-1}= 31/5 is x=(ln(3/13))/(ln(5))
Solve for x: 5^{x+1}+5+5^{x-1}= 31/5
The solution is x=(ln(3/13))/(ln(5))