Question

solve 5^{x+1} + 5^{2-x} = 5^{3} +1

Answer 1

5^x+1+5^2-x=5^3+5^0 (as 5^0 is 1)
so 5^x+1=5^3 and 5^2-x=5^0
5^x+1=5^3
as bases are equal equate powers
x=3-1=2
in second also 5^2-x=5^0
x becomes 2 only.
therefore the value of x in this problem is 2.and it is equal in both cases

Answer 2

5^x+1+5^2-x=5^3+1
5^x+1+5^2-x=5^3+5^0
5^x+1=5^3     5^2-x=5^0
x+1=3            2-x=0
x=2                x=2

Therefore, the value of x=2.