simplifying, functions and logarithms

[thepapercup]

Well, I have a test coming up soon and I would very much appreciate getting help on the many questions I'm going to be posting. I cannot, for the life of me, understand the way my math teacher tries to explain these problems and I'm terrified of failing that test. It's going to be worth 125 points and if I fail that test my grade will drop to an F. So thank you dearly to anybody who tries to help me.

So, here are a few examples of the questions that I need to know how to do:

Simplify
1.) 36[sup:1azoadkg]5/2[/sup:1azoadkg]
2.) 300[sup:1azoadkg]1/2[/sup:1azoadkg]
3.) The cubed root of 81y[sup:1azoadkg]12[/sup:1azoadkg]
4.) The fourth root of x[sup:1azoadkg]-1[/sup:1azoadkg] times the fourth root of 16x[sup:1azoadkg]-3[/sup:1azoadkg]

I also need help with functions. For example:

1.) Find the value of b when f(x)=5b[sup:1azoadkg]x[/sup:1azoadkg] and f(2/3)=80
2.) Graph each function and it's reflection over the line y=x. Is the reflection the graph of a function? Write yes or no.
a.) y=1.5[sup:1azoadkg]x[/sup:1azoadkg]
b.) y=2x[sup:1azoadkg]2[/sup:1azoadkg]-3
3.) True or False
The graph of y=ab[sup:1azoadkg]x[/sup:1azoadkg] is a reflection about the y-axis of the graph of y=ab[sup:1azoadkg]-x[/sup:1azoadkg]
4.) Write an equation of the inverse for each function
a.) y=2.3x-4
b.) y=x[sup:1azoadkg]3/2[/sup:1azoadkg]
c.) y=3x[sup:1azoadkg]3[/sup:1azoadkg]+1

Logarithms
(if you could help me figure out what I'm supposed to be pressing on my calculator that would be very helpful also.)

Evaluate:
1.) log1/1000
2.) In12
3.) log[sub:1azoadkg]8[/sub:1azoadkg] 512

Evaluate to three decimal places:
(if I just know how to evaluate like the three above I could do these ones)

1.) log[sub:1azoadkg]2[/sub:1azoadkg] 42
2.) log[sub:1azoadkg]7[/sub:1azoadkg] 24
3.) log[sub:1azoadkg]5[/sub:1azoadkg] 3/4

Solve:
1.) log[sub:1azoadkg]x[/sub:1azoadkg]343=3
2.) e[sup:1azoadkg]2[/sup:1azoadkg]x=1/e[sup:1azoadkg]-6[/sup:1azoadkg]
3.) 10[sup:1azoadkg]x[/sup:1azoadkg]=28
4.) log[sub:1azoadkg]x[/sub:1azoadkg]x+log[sub:1azoadkg]2[/sub:1azoadkg](x+2)=3
5.) log[sub:1azoadkg]3[/sub:1azoadkg](7m)=1+log[sub:1azoadkg]3[/sub:1azoadkg](m+2)

Write each expression in terms of log[sub:1azoadkg]5[/sub:1azoadkg]M and log[sub:1azoadkg]5[/sub:1azoadkg]N:
1.) log[sub:1azoadkg]5[/sub:1azoadkg]M[sup:1azoadkg]3[/sup:1azoadkg]N
2.) log[sub:1azoadkg]5[/sub:1azoadkg]M/the fourth root of N

Simplify:
log[sub:1azoadkg]4[/sub:1azoadkg]4+log[sub:1azoadkg]4[/sub:1azoadkg]32-log[sub:1azoadkg]4[/sub:1azoadkg]8

True of False:
log[sub:1azoadkg]1/5[/sub:1azoadkg]=log[sub:1azoadkg]1[/sub:1azoadkg]/log[sub:1azoadkg]5[/sub:1azoadkg]

 

[mmm4444bot]

Hello Lori:

These exercises cover several weeks of instruction. There's no way that I'm going to type up explanations covering these many topics, rules, properties, and algebraic methods.

It would be faster, for me, to drive to Gold Bar.

Calculator keys vary from model to model; I don't know what kind of calculator you have. Can't you experiment until you get the machine to display what you want?

The scientific calculator bundled with Windows has keys labeled [ln] and [log].

Start > All Programs > Accessories > Calculator

The first time you use the Windows' calculator, it defaults to Standard View. You need to manually switch it to Scientific View. Click 'View' on the menu bar, and select Scientific.

To get base-10 logarithms, use the [log] key; to get natural logarithms, use the [ln] key.

EXAMPLE: 10 needs to be raised to what number to equal 1,000?

The answer is log(1000).

(You can clear the Windows' calculator by hitting the ESC key on your keyboard.)

Type 1000.

Click the [log] button.

The calculator displays 3.

log(1000) = 3

So, 10 needs to be raised to the third power, in order to equal 1,000.

The natural logarithm button works the same way.

ln(50) = ?

Hit ESC.

Type 50.

Click [ln].

The calculator displays 3.9120230054281460586187507879106 .

I will do one of your exercises for you.

This is the second exercise #1.

Given: f(x) = 5 * b^x

Given: f(2/3) = 80

Find b.

The statement f(2/3) = 80 is function notation.

It tells us that the expression 5 * b^x will equal 80 if we let x be 2/3.

Let's do that.

5 * b^(2/3) = 80

Now we have an equation with only the symbol b. (The number that b represents is some constant.)

First, let's isolate b^(2/3). We can do this by dividing by 5.

[5 * b^(2/3)]/5 = 80/5

On the left-hand side, the fives cancel.

b^(2/3) = 16

Raise both sides to the 3/2 power (this will change the exponent on b from 2/3 to 1).

[b^(2/3)]^(3/2) = 16^(3/2)

Now on the left-hand side, we use the property of exponents that tells us to multiply the exponents together when one power is raised to another.

Since (2/3) * (3/2) = 1, we get b^1 on the left-hand side.

b = 16^(3/2)

This value can be simplified.

b = 64

CHECK: Now that we know that b represents the number 64, we can write the definition of function f.

f(x) = 5 * 64^x

Is f(2/3) equal to 80?

f(2/3) = 5 * 64^(2/3) = 5 * [(64^2)^(1/3)] = 5 * 4096^(1/3) = 5 * 16 = 80

The answer checks. b = 64.

 

[stapel]

I cannot, for the life of me, understand the way my math teacher tries to explain these problems....

Ah. So you've been needing tutoring for the last few weeks or months. That's going to be hard to "make up" at the last minute. :shock:

As was mentioned in the previous reply, it is not reasonably feasible to attempt to teach courses within this environment. However, if you are willing to invest the time and effort, you might be able to get by with online self-teaching.

For exponents and radicals (the first problem set), try here:

. . . . .Google results for "exponents"
. . . . .Google results for "radicals"

To learn about functions and symmetry, try here:

. . . . .Google results for "functions"
. . . . .Google results for "function notation"
. . . . .Google results for "symmetry"
. . . . .Google results for "function reflection"
. . . . .Google results for "function inverse"
. . . . .Google results for "composition functions"

To learn about logs and exponentials, try here:

. . . . .Google results for "logarithms"
. . . . .Google results for "log rules"
. . . . .Google results for "exponentials"
. . . . .Google results for "solving log equations"

Good luck!