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Logarithm Problem

  1. Jun 28, 2009 #1
    1. The problem statement, all variables and given/known data
    1) Solve the equation using the exponential form of the equation.

    Log2(2-5x)=7

    2) Rewrite as a single logarithmic expression:

    3log x +(1/2)log z



    2. Relevant equations



    3. The attempt at a solution

    1) I have no idea how to solve this.

    2) I know that two logarithms multiply to add, but these have different bases so I do not know what to do.

    Thanks.
     
    Last edited: Jun 28, 2009
  2. jcsd
  3. Jun 28, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    Here is a hint.

    [tex]a^b =c \Rightarrow b= log_a c[/tex]

    they are in the same base. Logx usually means log10x.

    Use the rule

    [tex]rlog_a x = log_a x^2[/tex]
     
  4. Jun 29, 2009 #3

    Mentallic

    User Avatar
    Homework Helper

    I'll just fix up rock.freak667's little typo there.

    What was meant to be said is: [tex]r.log_a(x)=log_a(x^r)[/tex]

    Coupled with the rule that [tex]log_a(b)+log_a(c)=log_a(bc)[/tex]

    You should have no problem solving the second one :smile:
     
  5. Jun 29, 2009 #4

    Mark44

    Staff: Mentor

    I think it might be helpful to add that a logarithm can be thought of as the exponent on the base (the number raised to a power) that results in a particular number. So for example, log10100 means the exponent on 10 that results in 100. In other words, this logarithm is the answer to the question 10? = 100. Pretty clearly, the placeholder represented by ? is 2.

    Every equation of the form logbx = y can be rewritten as an equivalent exponential equation by = x, and vice versa, with the only restrictions being that b > 0, and b[itex]\neq[/itex] 1, and x > 0.
     
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