If it is given that \(5^{x + 1} + 5^x = 150\), then the value of x is equal to
A
3
B
4
C
1
D
2
E
\(\frac{1}{2}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(5^{x + 1} + 5^x = 150\)
according to the laws of indices
\(5^1(5^x) + 5^x = 150\)
let \(5^x\) = y
5(y) + y = 150
6y = 150
y = \(\frac{150}{6}\)
= 25
but y = \(5^x\) = 25
\(5^x\) = 25 = \(5^2\)
equating powers since bases are the same
x = 2
Source: Myschool Past Questions Archive (Record #32631)