What is the first step in solving in(x - 1) = in6 - inx for x?

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.

Step-by-step explanation:

Solution:

1. x = 3

2. y = (-2/3)x + 2

3. y = -2

4. y = 3x + 5

5. y = -2x + 5 (im assuming the minus is an equal sign?)

6. y = 3

Step-by-step explanation:

1. for this question, look at the graph, and find the slope. there is no slope, right? because its just a straight vertical line. this is called an undefined slope. you only know the x value, which is 3, and the y values are infinite. since you cant really make an equation, it would just be x = 3, because that's all you know from the graph.

2. For this graph, you have to count boxes. Slope is "rise over run", which means the number of boxes you go up, is the numerator for the slope, and the number of boxes you go to the left or right is the denominator. So in this graph, put your finger on any point on the line you know, like (3,0). Then, count how many boxes you have to go up and to the left to get to another point, like (0,2). You went up 2 boxes, and went to the left 3 times right? So the slope would be 2/3, but since you went to the LEFT, its negative. So that's the slope. The y intercept, is just visible on the graph. You can see the line intersects the y line at (0,2), so the y intercept is 2.

3. This is the same as number one, but you only know the one y value, which is -2. This graph is called a zero slope, because it doesn't go up or down. So since all you know is y = -3, that's your forumla.

4. Follow the same steps as number 2! you'll get the hang of it :) (start from a point that's really clear, like (-1,2), which is right on the line, and then count to antoher point, like (0,5), which is also the y intercept.

5 & 6. These questions just give you the slope, and the y intercept, so its easy! the formula is y = mx + b. m is the slope, and b is the intercept! just plug in and you get the answer :)