Solve the equation. Find the exact solution. $\log x + \log ( x + 1 ) = \log 20$
A) $6$
B) $4$
C) $19$
D) $20$
E) $2$

Question

Quizplus · Accepted Answer

Using the logarithmic identity $\log(a)+\log(b)=\log(ab)$, we can simplify the equation as follows:
$$\log x + \log(x+1) = \log 20$$
$$\log x(x+1) = \log 20$$
$$x(x+1) = 20$$
$$x^2+x-20=0$$
$$(x+5)(x-4)=0$$
Since $x$ must be positive, we choose $x=4$. Thus, the only correct choice is B.

Solve the Equation log⁡x+log⁡(x+1)=log⁡20\log x + \log ( x + 1 ) = \log 20logx+log(x+1)=log20

Solve the Equation $\log x + \log ( x + 1 ) = \log 20$