Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4
decimal places if necessary.
-$\ln x + \ln ( x + 4 ) = \ln ( 2 x + 35 )$
A) $\{ 5 \}$
B) $\{ 5 , - 7 \}$
C) $\{ - 7 \}$
D) $\{ - 5,7 \}$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the equation $\ln x + \ln ( x + 4 ) = \ln ( 2 x + 35 )$ simplifies to $\ln(x(x + 4)) = \ln(2x + 35)$. This implies $x(x + 4) = 2x + 35$, leading to a quadratic equation $x^2 + 4x - 2x - 35 = 0$, which simplifies to $x^2 + 2x - 35 = 0$. Factoring or using the quadratic formula gives $x = 5$ as the only positive, valid solution since the logarithm of a negative number is undefined.

Solve the Equation ln⁡x+ln⁡(x+4)=ln⁡(2x+35)\ln x + \ln ( x + 4 ) = \ln ( 2 x + 35 )lnx+ln(x+4)=ln(2x+35)

Solve the Equation $\ln x + \ln ( x + 4 ) = \ln ( 2 x + 35 )$