Question

What is the first step in solving ln(x − 1) = ln6 − lnx for x?

Answer 1

The first step to solving this problem is Multiplying In(x-1).

Answer 2

The first step is to apply the laws of logarithms and write (In 6 - In x) as a single logarithms.

Solving he equation, x = 3 or x = -2.

Explanation:

In (x - 1) = In 6 - In x

To solve this, we first apply the laws of logarithms and write (In 6 - In x) as a single logarithms.

In 6 - In x = In (6 ÷ x) = In (6/x)

In |(x - 1)| = In |(6/x)|

We can then say that

(x - 1) = (6/x)

x(x - 1) = 6

x² - x - 6 = 0

x² - 3x + 2x - 6 = 0

x(x - 3) + 2(x- 3) = 0

(x - 3)(x + 2) = 0

x = 3 or x = -2

Hope this Helps!!!