Jerome solved the equation below by graphing.

log_2x+log_2(x-2)=3

Which of the following shows the correct system of equations and solution?

a.) y_1=logx/log2 +log(x-2)/log2 y_2=3, x=3

b.) y_1=logx/log2 + log(x-2)/log2 y_2=3, x=4

c.) y_1=logx+log(x-2) y_2=3, x=33

d.) y_1=logx +log(x-2) y_2=3, x=44

Question

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Respuesta :

LammettHash LammettHash · Answer 1 · 2019-01-24T18:15:46+01:00

Jerome rewrote the logarithms as

[tex]\log_2x=\dfrac{\log x}{\log2}[/tex]

[tex]\log_2(x-2)]=\dfrac{\log(x-2)}{\log 2}[/tex]

which eliminates C and D.

Solve the equation:

[tex]\log_2x+\log_2(x-2)=\log_2x(x-2)=3\implies 2^{\log_2x(x-2)}=2^3\implies x(x-2)=8[/tex]

[tex]\implies x^2-2x-8=(x-4)(x+2)=0\implies x=4\text{ or }x=-2[/tex]

[tex]\log_b(-2)[/tex] is undefined for any base [tex]b[/tex] (where the logarithm is real-valued), so we omit that solution.

This makes B the answer.

tardymanchester tardymanchester · Answer 2 · 2019-02-28T11:28:23+01:00

Answer:

Option b - [tex]y_1=\frac{\log x}{\log 2}+\frac{\log (x-2)}{\log 2}, y_2=3, x=4[/tex]

Step-by-step explanation:

Given : Jerome solved the equation below by graphing.

[tex]\log_2x+\log_2(x-2)=3[/tex]

To find : Which of the following shows the correct system of equations and solution?

Solution :

Two system of equations formed from given equation,

[tex]y_1=\log_2x+\log_2(x-2)[/tex]

[tex]y_1=\frac{\log x}{\log 2}+\frac{\log (x-2)}{\log 2}[/tex] ......[1]

[tex]y_2=3[/tex] .........[2]

Now, we plot these two equations and the intersection of these two equation is the solution.

The intersection point is (4,3)

Therefore, The solution of given equation is x=3

Hence, Option b is correct.