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

What Is The Solution Set To This Equation1054 3 1087 class=

Sagot :

ANSWER

[tex]C.\text{ }x=1\text{ and }x=-4[/tex]

EXPLANATION

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

[tex]\log_4(x+3)+\log_4x=1[/tex]

According to the laws of logarithm, we have that:

[tex]\begin{gathered} \log_ax+\log_ay=\log_a(x*y) \\ \\ and \\ \\ \log_aa=1 \end{gathered}[/tex]

Therefore, we can rewrite the equation as follows:

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

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

[tex](x+3)*x=4[/tex]

Simplify and solve for x:

[tex]\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}[/tex]

Hence, the correct answer is option C.

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