Respuesta :

mberisso

Answer:

x = 4

which agrees with the third listed answer among the given options

Step-by-step explanation:

We can re-write the logarithmic equation using the properties of logarithms:

[tex]2\,log(x)=log(8)+log(x-2)\\log(x^2)=log(8*(x-2))\\log(x^2)=log(8x-16)[/tex]

Therefore, the arguments of the log functions must also be equal (and we can solve for "x" by noticing that this expression is the perfect square of a binomial:

[tex]x^2=8x-16\\x^2-8x+16=0\\(x-4)^2=0[/tex]

and for this equation to verify, x must be 4

CHERLYNnotCHERRY

Answer:

The value of x is 4.

Step-by-step explanation:

You have to use Logarithm Laws :

[tex] log( {a}^{n} ) \: ⇒ \: n log(a) [/tex]

[tex] log(a) + log(b) \: ⇒ \: log(a \times b) [/tex]

So for this question :

[tex]2 log(x) \: ⇒ \: log( {x}^{2} ) [/tex]

[tex] log(8) + log(x - 2) \: ⇒ \: log(8(x - 2)) [/tex]

[tex] log( {x}^{2} ) = log(8x - 16) [/tex]

Next you have to cut out the log :

[tex] {x}^{2} = 8x - 16[/tex]

Then, you have to make the equation equals 0 :

[tex] {x}^{2} - 8x + 16 = 0[/tex]

Lastly, you have to solve it :

[tex] {x}^{2} - 4x - 4x + 16 = 0[/tex]

[tex]x(x - 4) - 4(x - 4) = 0[/tex]

[tex](x - 4)(x - 4) = 0[/tex]

[tex]x = 4[/tex]

Otras preguntas