Stuck - Algebra 2

**VintageSummer** · May 29th 2008, 04:01 PM

First, let me explain my situation so you can understand what I need first (if you want get to the point you can skip this part and see what I need help with). I am homeschooled. Today was the last day of school. Not only am I homeschooled, which in homestudies you are required to finish a book, but I'm also taking A-G (college prep) and my teacher is not very.... well he does not really cut me very much slack where it is needed. Which brings up my dilemma. I was going to spread out algebra 2 over 3 semesters, 1 year and half. But it looks like next year I do not have to take Algebra 2 (keep going) if I take another math course (I am taking art based Geometry, no functions, equations or mumbo jumbo that I know of - it is actually relevant to what I actually want to do with my life -> art) BUT I am 2 chapters behind and if I do not complete the 2 chapters over the summer I will get an incomplete, meaning an F and I won't get any credits, meaning this past year would have been a waste. So I am going to try to get at least a C or a D in math, by trying to complete chapter 8 and 9. What I have been doing to move more quickly is I have been reading the sections, learning the material, then doing the chapter test (50 questions about) which I have to get 100% on to pass (if I get 1 wrong I have to work it out and re-do the problem until I get it right) Here is the problem though I am on chapter 8 and I am totally stuck. I do not get anything. I even tried paying my older brother whom is a big brainiac to do it for me (heh I know I'm bad) but he couldn't even figure it out... I tried going to every math help site imaginable and read through their explanations on the subject and I still did not understand. Plus most of the things I did learn would not help me with the problems in the Chapter Test. By now you are probably saying "Get to the friggen point already!" (I know I should not have posted this much - but it might help you understand a little more what I need and why) Ok I will.

What I need help on is Exponential and Logerithmic Functions in Algebra 2. I am going to give an example of 1 problem from each little category in the chapter test and I need someone to PLEASE explain to me how I am supposed to tackle the problem (step by step), so it will help me with the rest of the problems.

First part:
Evaluate each function to the nearest hundreth for x= 0,1,2,3,4,5. Graph each function.
One of the problems is: y=3(0.25)^x

Write an exponential function of the form y=ab^x that has a graph through the given points.
One problem is: (-2, 2/25), (1, 10)

Describe how the graph of each function is related to the graph of its parent function.
One problem is: y=3^x+2

Graph Each Logarithmic function.
One problem is y= log9x

Use the properties of logarithms to rewrite each logarithmic expresson.
One problem is: log24+3 log29

Use the properties of logarithms to evaluate each expresson.
One problem is log327 - log39

Solve Each Expresson.
(3/4)^x=81
or
log 4x = 3

Use the Change of Base Formula to rewrite each expresson using common logarithms.
log316

Use the properties of logarithms to simpliphy each equation and solve it. Round to thousandths.
In 2 + In x = 1

If someone could explain to me how to do these problems so I can use those instructions to help me figure out the rest. It would also be great if I could post what I get so someone could tell me if they are right or not - like I said I need to get 100% in order to be done.

**Jonboy** · May 29th 2008, 05:09 PM

i fully read your post, as long as it was lol.
i'll explain the ones that i understand.

do you have a graphing calculator? that could help a lot on the graphing part.

Use the properties of logarithms to rewrite each logarithmic expression.
One problem is: $log_{2}4 + 3 log_{2}9$

You can move the number in front of a log as an exponent.
So: $3 log_{2}9$ becomes $log_{2}9^{3}=log_{2}729$

Now you have: $log_{2}4 + log_{2}729$

Since the bases (twos) are the same, you can simplify that as:

$log_{2}(4)(729) = log_{2}2916$

Use the properties of logarithms to evaluate each expression.
One problem is $log_{3}27 - log_{3}9$

When you subtract logs, if they have the same base, you may divide what you're taking the log of.

So: $log_{3}\frac{27}{9} = log_{ \not 3}{\not 3} = log 1$

This is a property: $log 1 = 0$

So your answer is 0.

Solve Each Expression.
(3/4)^x=81
or
log 4x = 3

I'll pick the first.

You have: $\bigg(\frac{3}{4}\bigg)^{x} = 81$

Change the form to logarithmic:

$log_{base} solution = exponent \Rightarrow log_{\frac{3}{4}}81 = x$

Use the Change of Base Formula: $log_{b} a = \frac{log a}{log b}$

So use a calc and evaluate: $\frac{log 81}{log \frac{3}{4}}$

Use the Change of Base Formula to rewrite each expresson using common logarithms.
log_{3}16

You have a table with values, right?

First use change of base formula above: $\frac{log 16}{log 3}$

You can make that $\frac{log4 + log4}{log 3}$

Plug the values of log 4 and log 3 into the equation and simplify.

Use the properties of logarithms to simplify each equation and solve it. Round to thousandths.

In 2 + In x = 1

Use the property: $ln\,a + ln\,b = ln\,(a)(b)$

Thus: $ln\,2x = 1$

Raising both side to the power of $e$ gets rid of the $ln$ .

So: $2x = e \Rightarrow x = \frac{e}{2}$

When rounding you should get: $1.359$

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