## What is the first step in solving In(x – 1) = In6 – Inx for x?

Question

What is the first step in solving In(x – 1) = In6 – Inx for x?

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2 weeks 2021-09-10T15:10:01+00:00 2 Answers 0

The first step would to be use quotient rule.

3

Step-by-step explanation:

ln(x-1)=ln(6)-ln(x)

The first step would to be use quotient rule there on the right hand side:

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

*Quotient rule says ln(a/b)=ln(a)-ln(b).

Now that since we have ln(c)=ln(d) then c must equal d, that is c=d.

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

implies

x-1=6/x

So you want to shove a 1 underneath the (x-1) and just cross multiply that might be easier. Cross multiplying: Multiplying/distribute[/tex] Subtract 6 on both sides: Now this is not too bad to factor since the coefficient of x^2 is 1.  All you have to do is find two numbers that multiply to be -6  and add up to be -1.

These numbers are -3 and 2 since -3(2)=-6 and -3+2=-1.

So the factored form of our equation is This implies that x-3=0 or x+2=0.

So solving x-3=0 gives us x=3 (just added 3 on both sides).

So solve x+2=0 gives us x=-2 (just subtracted 2 on both sides).

We need to see if these are actually the solutions by plugging them in.

Just a heads up: You can’t do log(negative number).

Checking x=3:

ln(3-1)=ln(6)-ln(3)

ln(2)=ln(6/3)

ln(2)=ln(2)

This is true.

Checking x=-2:

ln(-2-1)=ln(6)-ln(-2)

ln(-3)=ln(6)-ln(-2)

We don’t need to go further -2 makes the inside of our logarithms negative above.

The only solution is 3.

2. Step-by-step explanation:

### The first step is to create the domain of this equation.  Solution: