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Math Help - Help needed with "Exponential and Logarithm Functions"

  1. #1
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    Help needed with "Exponential and Logarithm Functions"

    I don't really know where to start in solving this functions, any help would be much appriciated.

    Solve for x. log2(3x 8) ≥ 6
    Solve for x. log556x+1 = 13
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  2. #2
    MHF Contributor
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    Quote Originally Posted by 14041471 View Post
    Solve for x. log2(3x 8) ≥ 6
    As you learned when graphing log functions, the height of the line increases as the input value increases. So I believe we can convert the above to the following:

    . . . . . \log_2(3x\, -\, 8)\, \ge \,\log_2(2^6)

    ...and then equate the arguments:

    . . . . . 3x\, -\, 8\, \ge\, 2^6

    Solve the linear equation.

    Quote Originally Posted by 14041471 View Post
    Solve for x. log556x+1 = 13
    I will guess that the "556" is the base, and that the "1" is outside the log. Then solve by subtracting the 1 to the other side. Then raise each side as a power on 556:

    . . . . . 556^{\log_{556}(x)}\, =\, 556^{12}

    Simplify the left-hand side to get your answer.

    I wouldn't bother plugging that into your calculator, though...
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