Solve the equation.
-$\log _ { 2 } ( x + 4 ) = 1 + \log _ { 2 } ( x - 3 )$
A) $\{ - 7 \}$
B) $\{ - 10 \}$
C) $\{ 10 \}$
D) $\{ 7 \}$

Question

Quizplus · Accepted Answer

To solve the equation $\log_2(x + 4) = 1 + \log_2(x - 3)$, we first use the property of logarithms to combine the right side: $1 = \log_2(2)$ because $2^1 = 2$. This gives us $\log_2(x + 4) = \log_2(2) + \log_2(x - 3) = \log_2(2(x - 3))$. Since the bases are the same, we can set the arguments equal to each other: $x + 4 = 2(x - 3)$. Solving this equation, we get $x + 4 = 2x - 6$, which simplifies to $x = 10$. Therefore, the solution is $x = 10$.

Solve the Equation log⁡2(x+4)=1+log⁡2(x−3)\log _ { 2 } ( x + 4 ) = 1 + \log _ { 2 } ( x - 3 )log2​(x+4)=1+log2​(x−3)

Solve the Equation $\log _ { 2 } ( x + 4 ) = 1 + \log _ { 2 } ( x - 3 )$