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Math Help - Log questions, DID THEM ALL, Just need to make sure there correct?

  1. #1
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    Log questions, DID THEM ALL, Just need to make sure there correct?

    Hey guys I'm new here. How's everyone doing? I just finished doing a bunch of log problems. If you find any faults, please tell me. This test counts for a lot, and every correct answer is worth big.

    I wrote out all the questions, and at the bottom of each I wrote my answers in bold. Please guide me guys. I need to ace this.

    1-A bacteria divides into 4 new cells every 20 minutes. If the bacteria reproduces for x hours, find the
    exponential equation that represents the increase in population as a function of time.

    I found y= 12^x

    2- Simplify:
    A- (2/3)^2X+3 = (27/8)^3X-2
    I found x=0,27

    B- 3^x+3= 13574
    I found x= 5.6617

    3- Find the inverse of the following function: f (x)= log base5(3-x)
    I found y= -5^x + 3

    4- For the following function f(x)= 3 (1/2)^4x-1 + 5, State whether the statements are true or false. Correct the false ones.

    A. It is decreasing
    B. The ordinate is 8
    C. The equation of the asymptote is y=5
    D. It is always positive
    E. It has no abcissa at the origin

    I wrote true for A, C, D and E, and I wrote the ordinate is 11 for B

    5- Find the equation of the following log function with an asymptote of x= -5.625 and passing through the point (10,3)
    I found y= log2.5 (x+5.625)

    6- Martha brought a bond for 1500.00$ at an annual rate of 4.8%, compounded semi annually. Find the rule that
    describes the value as a function of the number of years. Using the rule, find the value in 10 years.

    I found the rule was y= 1500. 1.024^2x, so in 10 years
    y= 1500 . 1.024^20= 1901,47$

    7- The following rule is used for calculating the number of years (y) it takes for a bond to reach a certain amount (x)
    y= 96.64logx - 460.34
    Calculate how much time it would take to reach 65000 and 85000.

    I put in 65000 and 85000 for x, and got 4.78 and 16.04.

    8. Find the value of the following expression:
    8(log4 32 + log2 8) - (log2 16)^2

    I found 28

    Thanks in advance guys!
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  2. #2
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    Quote Originally Posted by helpmeplz View Post
    ...
    2- Simplify:
    A- (2/3)^(2X+3) = (27/8)^(3X-2)
    I found x=0,27

    B- 3^(x+3)= 13574
    I found x= 5.6617

    ...
    All your considerations and calculations are OK!

    You only should use brackets to make clear which term belongs to an exponent. (See coorections in red)
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