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    Ok here's the question

    log(base2)x=12 so find the following:
    A) log(base2)x3
    B)log(base2)16x
    C)log(base2)rootx

    Im struggling on how to start and what is actually being asked of me.

    Do I need to find x? Is there a particular rule of logs I should be using?

    I've got some brilliant help on TSR in the past so hoping you guys can help me again on this!

    Thanks in advance
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    Just use these laws of logarithms:

    \log_2 (ab) = \log_2 a + \log_2 b

    \log_2 a^n = n \log_2 a
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    first log(base2)x=12 means 2^12 = x
    so for A, using the definition again 2^(something) =x^3 now it should be clear then how to proceed with the rest
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    (Original post by Mr M)
    Just use these laws of logarithms:

    \log_2 (ab) = \log_2 a + \log_2 b

    \log_2 a^n = n \log_2 a
    Okay, so for \log_2 (ab) = \log_2 a + \log_2 b

    This means \log_2 (16x) = \log_2 16 + \log_2 x?

    And \log_2 a^n = n \log_2 a

    Means \log_2 x^3 = 3 \log_2 x
    If so, then what? I don't understand what the acutal answer is supposed to me? And which rule do I use for the square root of x one?
    (Sorry for the continuous questions!)
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    (Original post by breakeven)
    Okay, so for \log_2 (ab) = \log_2 a + \log_2 b

    This means \log_2 (16x) = \log_2 16 + \log_2 x?

    And \log_2 a^n = n \log_2 a

    Means \log_2 x^3 = 3 \log_2 x
    If so, then what? I don't understand what the acutal answer is supposed to me?
    So you are very close now.

    What does \log_2 x = (massive hint, you are told the answer in the question) ?
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    (Original post by Ayakashi)
    first log(base2)x=12 means 2^12 = x
    so for A, using the definition again 2^(something) =x^3 now it should be clear then how to proceed with the rest
    So, x=4096?

    and Log(base2)x3=36?
    Is 36 the actual final answer?
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    (Original post by Mr M)
    So you are very close now.

    What does \log_2 x = (massive hint, you are told the answer in the question) ?
    I got a) = 36
    b) = 16
    and c) = 6

    Is that right?
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    (Original post by breakeven)
    I got a) = 36
    b) = 16
    and c) = 6

    Is that right?
    Yes.
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    (Original post by breakeven)
    So, x=4096?

    and Log(base2)x3=36?
    Is 36 the actual final answer?
    I wouldn't do this. It is correct but unnecessarily complicated.
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    (Original post by Mr M)
    Yes.
    Thanks a million for your help and patience, you rock!
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    (Original post by breakeven)
    Thanks a million for your help and patience, you rock!
    :rock:
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    (Original post by Mr M)
    :rock:
    Last question on my sheet and I'm stuck again

    Wondered if you might want to help out again, its fine if you don't

    f(x)=x3-x2-7x+c
    f(4)=0
    a) Find C (which I got -20 for)
    b) Factorise f(x) as the product of a linear factor and a quadratic factor
    c) hence show that, apart from x=4, there are no real values of x for which f(x)=0

    B+C are confusing me.
    I guessed that I needed to find the quotient using (x-4) and then factorise it using the quadratic formula which didnt work.

    Not sure what it's asking me to do now:/
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    (Original post by breakeven)
    Last question on my sheet and I'm stuck again

    Wondered if you might want to help out again, its fine if you don't

    f(x)=x3-x2-7x+c
    f(4)=0
    a) Find C (which I got -20 for)
    b) Factorise f(x) as the product of a linear factor and a quadratic factor
    c) hence show that, apart from x=4, there are no real values of x for which f(x)=0

    B+C are confusing me.
    I guessed that I needed to find the quotient using (x-4) and then factorise it using the quadratic formula which didnt work.

    Not sure what it's asking me to do now:/
    You know that f(4)=0 so (x-4) is a factor (from factor theorem).

    f(x)=(x-4)(Ax^2+Bx+C)

    You should be able to write down the values of A and C immediately and figure out B (expand the brackets and equate coefficients if you need to).
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    (Original post by Mr M)
    You know that f(4)=0 so (x-4) is a factor (from factor theorem).

    f(x)=(x-4)(Ax^2+Bx+C)

    You should be able to write down the values of A and C immediately and figure out B (expand the brackets and equate coefficients if you need to).
    So, (x-4)(x2+3x+5)?

    A=1 B=3 C=5?

    And for part c? xx
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    (Original post by breakeven)
    And for part c? xx
    What method do you know that shows a quadratic has no real roots?
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    (Original post by Mr M)
    What method do you know that shows a quadratic has no real roots?
    Do you mean show that the discriminant is less than 0?
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    (Original post by breakeven)
    Do you mean show that the discriminant is less than 0?
    :yes:
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    (Original post by Mr M)
    :yes:
    I'm sending you lots of air hugs right now! I appreciate your help and explanations, they really do help so much
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    (Original post by breakeven)
    I'm sending you lots of air hugs right now! I appreciate your help and explanations, they really do help so much
    Ok - you are welcome.
 
 
 
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