Question

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

A.
Simplify the left side using the "log of a difference is the quotient of the logs" property.
B.
Simplify the right side using the "difference of two logs is the log of the product" property.
C.
Simplify the right side using the "difference of two logs is the log of the quotient" property.
D.
Simplify the left side using the "log of a difference is the difference of the logs" property.

Answer 1

Option C - Simplify the right side using the "difference of two logs is the log of the quotient" property.

Explanation:

Given : Expression
`\ln (x-1)=\ln 6-\ln x`

To find : What is the first step in solving the expression ?

Solution :

Expression
`\ln (x-1)=\ln 6-\ln x`

Step 1 - Simplify the right side using the "difference of two logs is the log of the quotient" property.

i.e.
`\ln a-\ln b=\ln((a)/(b))`

Apply the first step we get,

`\ln (x-1)=\ln((6)/(x))`

Therefore, Option C is correct.