If log ₅ (x²+x)-log ₅(x+1)=2, then the value of x is · ABC26GN2066

Subject: General Aptitude · Chapter: Logarithms · Exam: M.B.A. 2007

If $\log _{5}\left(x^{2}+x\right)-\log _{5}(x+1)=2$, then the value of $x$ is

(a)5

(b)10

(c)25

(d)32

Answer

Answer (as printed): C

Explanation

$\log _{5}\left(x^{2}+x\right)-\log _{5}(x+1)=2$ $$\begin{aligned} & \Rightarrow \log _{5}\left(\frac{x^{2}+x}{x+1}\right)=2 \Rightarrow \log _{5}\left[\frac{x(x+1)}{x+1}\right]=2 \\ & \Rightarrow \log _{5} x=2 \Rightarrow x=5^{2}=25 \end{aligned}$$

Explanation as extracted from the printed page; notation may be imperfect.

Study loop for Logarithms

1. Practise the PYQsPrevious-year questions, with answers

· Browse this chapter in the app