Question

Solve the following equation for x

Answer 1

C

Explanation:

Using the laws of logarithms

• log x + log y ⇔ log(xy)

• log x = log y ⇒ x = y

Given

logx + log(x - 3) = log 3x

log x(x - 3) = log 3x, hence

x(x - 3) = 3x

x² - 3x = 3x ( subtract 3x from both sides )

x² - 6x = 0 ← factor out x from each term

x(x - 6) = 0

Equate each factor to zero and solve for x

x = 0

x - 6 = 0 ⇒ x = 6

Solutions are x = 0, x = 6 → C

Answer 2

Answer: OPTION A

Explanation:

You need to remember the logarithms properties:

`log(a)+log(b)=log(ab)\\\\log(a)-log(b)=log((a)/(b))\\\\log(a)^b=b*log(a)`

Rewrite the equation:

`log(x(x-3))=log(3)+log(x)`

Like this logarithm has base 10, you can make this procedure:

`log(x(x-3))-log(x)=log(3)`

`log((x(x-3)))/((x))=log(3)`

`log(x-3)=log(3)`

`10^(log((x-3)))=10^(log(3))`

Then:

`(x-3)=3`

Now you need to solve for the variable "x":

`x=3+3\\x=6`