Question

What is the solution set to this equation?1054(= + 3) + 108.7

Answer 1

`C.\text{ }x=1\text{ and }x=-4`

Step-by-step explanation

We want to find the solution set to the equation given:

`\log_4(x+3)+\log_4x=1`

According to the laws of logarithm, we have that:

`\begin{gathered} \log_ax+\log_ay=\log_a(x*y) \\ \\ and \\ \\ \log_aa=1 \end{gathered}`

Therefore, we can rewrite the equation as follows:

`\log_4[(x+3)*x]=\log_44`

Since the logarithms on both sides have the same base, it implies that:

`(x+3)*x=4`

Simplify and solve for x:

`\begin{gathered} x^2+3x=4 \\ \\ x^2+3x-4=0 \\ \\ x^2+4x-x-4=0 \\ \\ x(x+4)-1(x+4)=0 \\ \\ (x-1)(x+4)=0 \\ \\ x=1\text{ and }x=-4 \end{gathered}`

Hence, the correct answer is option C.