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Math Help - Stuck - Algebra 2

  1. #1
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    California
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    Stuck - Algebra 2

    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.
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  2. #2
    Member Jonboy's Avatar
    Joined
    May 2007
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    South Point
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    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
    Last edited by Jonboy; May 29th 2008 at 05:17 PM. Reason: clarifying "taking the e"
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