Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
-$\log ( x + 20 ) - \log 4 = \log ( 7 x + 2 )$
A) $\left\{ \frac { 4 } { 9 } \right\}$
B) $\{ 26 \}$
C) $\left\{ - \frac { 4 } { 9 } \right\}$
D) $\{ - 26 \}$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the equation can be simplified to $\log\left(\frac{x + 20}{4}\right) = \log(7x + 2)$. Setting the arguments equal gives $\frac{x + 20}{4} = 7x + 2$. Solving for $x$ yields $x = \frac{4}{9}$, which is the only solution that fits the domain of the original logarithmic expressions.

Solve the Logarithmic Equation log⁡(x+20)−log⁡4=log⁡(7x+2)\log ( x + 20 ) - \log 4 = \log ( 7 x + 2 )log(x+20)−log4=log(7x+2)

Solve the Logarithmic Equation $\log ( x + 20 ) - \log 4 = \log ( 7 x + 2 )$