Homework Help: I can't make sense of this log property explanation?

1. Sep 29, 2011

roger12

1. The problem statement, all variables and given/known data

I decided to cram these two unrelated question into one post, because they are too small and I don't want to crowd the forum with my many little bitty questions.

1. log(base A) of B= 1/[log(base B) of A]

because: if log(base B) of A=C, then B^C=A and so B=A^1/C

Hence, log(base A) of B= 1/C= 1/[log(base B) of A]

2. plot the graph of:

x^2+x+1: x<1, x=1 for [-3, 4] with intervals of 0.5

It's a part of a bigger graph.

2. Relevant equations

3. The attempt at a solution

1. I don't see how introducing C as equal to a different base and then carrying out a bunch of algebraic manipulations prove anything. Am I missing something here? Thank You.

2. x,y pairs (-3, 7), (-2, 3), (-1,1) I chose the whole numbers for x, because they are more convenient to me. If you look at this part of the graph in my book it goes through different points. Can, you please tell me where I went wrong? Thanks.

2. Sep 29, 2011

eumyang

Remember the for logarithms,
logn x = y iff ny = x

So, using this, if
logB A = C, then BC = A.

From
BC = A,
raise both sides to the exponent of 1/C, so
(BC)1/C = (A)1/C,
or B = A1/C.

Using that definition of logarithms I gave earlier, Since
B = A1/C,
logAB = 1/C.

Substitute logB A = C into the fraction, so
logAB = 1/(logB A)

3. Sep 29, 2011

Staff: Mentor

Apparently you are graphing the equation y = x2 + x + 1, although what you showed is not an equation.

What does this part (in red) mean?
The points you show, (-3, 7), (-2, 3), (-1,1), are on the graph of y = x2 + x + 1. Does the graph in your book come from this equation?

4. Sep 29, 2011

roger12

Awesome!!! Why I forgot "If A=B^C, then C=log(base B)A" is beyond me.

5. Sep 29, 2011

roger12

The parts in red mean x is less than or equal to 1.

And it IS an equation :

y=x^2+x+1: x< or =1

and

y= 3-x : x>1

for [-3, 4]

y is defined differently for different values of x. But both expressions are the parts of the same equation. The part of the graph defined by y= 3-x : x>1 for [-3, 4] looks right, but the other part defined by y=x^2+x+1: x< or =1 for [-3, 4] doesn't sit on the points made up of ordered pairs above.