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Which of the following shows the true solution to the logarithmic equation solved below? log Subscript 2 Baseline (x) = log Subscript 2 Baseline (x + 7) = 3. log Subscript 2 Baseline left-bracket x (x + 7) right-bracket = 3. x (x + 7) = 2 cubed. x squared + 7 x minus 8 = 0. (x + 8) (x + 1) = 0. x = negative 8, 1

Sagot :

Answer:

x=1

Step-by-step explanation:

edge 2021

varshamittal029

The question was incomplete. Below you will find the missing image.

Option 2 is correct. i.e. x = 1

What is the correct answer ?

The given logarithmic equation is

[tex]log_{2}(x)+ log_{2}(x+7)=3[/tex]

⇒ [tex]log_{2}[x(x+7]=3[/tex]          [∵[tex]loga+logb=log ab[/tex]]

⇒ [tex]x(x+7)=2^{3}[/tex]

⇒ [tex]x^{2} +7x-8=0[/tex]

⇒ [tex](x+8)(x-1)=0[/tex]

⇒ x = -8, 1

At, x = 1

[tex]log_{2}(1)+ log_{2}(1+7)=3[/tex]

⇒ 0+3=3

⇒ 3=3

L.H.S = R.H.S, therefore x=1  is a solution of the given equation.

At, x = -8

[tex]log_{2}(-8)+ log_{2}(-8+7)=3[/tex]

⇒ [tex]log_{2}(-8)+ log_{2}(-1)=3[/tex]

Logarithmic functions are defined only for positive values.

So, x = -8 is not a solution of the given equation, i.e. a extraneous solution.

Hence, x= 1 is the only solution of the given equation.

Learn more about logarithmic function here :

https://brainly.com/question/27845085

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