Question

Order the steps to solve the equation

log(x2 − 15) = log(2x) form 1 to 5.

3
⇒ 2 x2 − 2x − 15 = 0

1
⇒ 5 Potential solutions are −3 and 5

5
⇒ 1 x2 − 15 = 2x

4
x − 5 = 0 or x + 3 = 0

2
⇒ 3 (x − 5)(x + 3) = 0

Answer 1

Rewrite the equation using the logarithmic property loga(b) = loga(c) if and only if b = c:

x2 - 15 = 2x

Move all the terms to one side of the equation:

x2 - 2x - 15 = 0

Use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a = 1, b = -2, and c = -15

x = (-(-2) ± sqrt((-2)^2 - 4(1)(-15))) / 2(1)

x = (2 ± sqrt(64)) / 2

x = 1 ± 4

Potential solutions are x = 5 and x = -3.

Check each potential solution in the original equation to see if it is valid. The logarithm of a negative number is undefined, so x = -3 is an extraneous solution. Therefore, the only valid solution is x = 5.

Plug x = 5 into the original equation to check:

log(5^2 - 15) = log(2(5))

log(10) = log(10)

Both sides are equal, so x = 5 is the correct solution.

Explanation: