To solve this equation, we first need to simplify it by combining like terms:
5^(x+1) + 5^x + 5^(x-1) = 31
Next, we can rewrite the terms in terms of the same base (5):
5 5^x + 5^x + (1/5) 5^x = 31
Simplify further:
5^x(5 + 1 + 1/5) = 31
5^x(25/5 + 5/5 + 1/5) = 31
5^x(31/5) = 31
Now we can solve for x:
5^x = 31 / (31/5)
5^x = 5
x = 1
Therefore, the solution to the equation is x = 1.
To solve this equation, we first need to simplify it by combining like terms:
5^(x+1) + 5^x + 5^(x-1) = 31
Next, we can rewrite the terms in terms of the same base (5):
5 5^x + 5^x + (1/5) 5^x = 31
Simplify further:
5^x(5 + 1 + 1/5) = 31
5^x(25/5 + 5/5 + 1/5) = 31
5^x(31/5) = 31
Now we can solve for x:
5^x = 31 / (31/5)
5^x = 5
x = 1
Therefore, the solution to the equation is x = 1.