Solve the equation.
-$\log _ { 4 } x + \log _ { 4 } ( x - 15 ) = 2$
A) 16
B) $1 , - 16$
C) $- 1,16$
D) 4

Question

Quizplus · Accepted Answer

Using the property of logarithms that allows combining two logs with the same base into a single log (logarithm of a product), the equation becomes $\log_4(x(x - 15)) = 2$. Converting from logarithmic to exponential form gives $4^2 = x(x - 15)$, which simplifies to $x^2 - 15x - 16 = 0$. Factoring or using the quadratic formula yields $x = 16$ as the only positive solution that makes sense in the context of the original logarithmic equation, since $\log_4(x - 15)$ must be defined (i.e., $x - 15 > 0$).

Solve the Equation log⁡4x+log⁡4(x−15)=2\log _ { 4 } x + \log _ { 4 } ( x - 15 ) = 2log4​x+log4​(x−15)=2

Solve the Equation $\log _ { 4 } x + \log _ { 4 } ( x - 15 ) = 2$