Question

Order the steps to solve the equation log3(x 2) = log3(2x2 − 1) from 1 to 6. 0 = (2x − 3)(x 1) 0 = 2x2 − x −3 Potential solutions are −1 and 3 2. 2x − 3 = 0 or x 1 = 0 x 2 = 2x2 − 1 3log3(x 2) = 3log3(2x2 − 1).

Answer 1

The exponent of the log rule says that the raising a logarithm with a number to its base is equal to the number.

Ordered steps to solve the equation are,

• 1)   $3^{\log_3(x^2) }=3^{\log_3(2x^2 - 1)}$
• 2) $0=2x^2-x-3$
• 3) $0=2x^2-x-3$
• 4) $(2x-3)(x+1)=0$
• 5)  $2x-3=0,\;\;\;\;x+1=0$
• 6) The potential solution are -1 and 3/2.

What is exponent of log rule?

The exponent of the log rule says that the raising a logarithm with a number to its base is equal to the number.

For example,

Let k is the number and a is the base thus,

$a^{log_a(k)}=k$

Given information-

The equation given in the problem is,

$\log_3(x^2) =\log_3(2x^2 - 1)$

Order of steps to solve the equation are-

• 1) Take the base 3 both the sides as,

         $3^{\log_3(x^2) }=3^{\log_3(2x^2 - 1)}$

• 2)The exponent of the log rule says that the raising a logarithm with a number to its base is equal to the number. Thus,

          $x^2+2=2x^2-1$

• 3) Take the variable with same power one side and solve them by equating to zero, we get,

           $0=2x^2-x-3$

• 4)Use the split the middle term method to make the group as,

          $(2x-3)(x+1)=0$

• 5) Equate the factors to the zero as,

            $2x-3=0\\x+1=0$

• 6) Solve the above factors as, we get the potential solution are -1 and 3/2.

Hence, ordered steps to solve the equation are,

• 1)   $3^{\log_3(x^2) }=3^{\log_3(2x^2 - 1)}$
• 2) $0=2x^2-x-3$
• 3) $0=2x^2-x-3$
• 4) $(2x-3)(x+1)=0$
• 5)  $2x-3=0,\;\;\;\;x+1=0$
• 6) The potential solution are -1 and 3/2.

Learn more about the rules of logarithmic function here;

https://brainly.com/question/13473114

Answer 2

Answer:

4

3

6

5

2

1

Step-by-step explanation: