If it is given that \(5^{x + 1} + 5^x = 150\), then the value of x is equal to
- 3
- 4
- 1
-
2
- \(\frac{1}{2}\)
The correct answer is: D
Explanation
\(5^{x + 1} + 5^x = 150\)
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