Precalculus

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Explain how to do these please.

1. solve x=log(base2)*1/8 by rewriting in exponential form.

2. Solve log(3x+1)=5

3. Solve log(base x)8=-1/2

  • Precalculus -

    x = log2 (1/2)^3

    x = 3 log2 (1/2)

    x/3 = log 2(1/2) = log 2 (1) - log2(2)

    but log2 (1) = 0 and log 2 (2) = 1
    so
    x/3 = -1
    x = -3

  • Precalculus -

    log(3x+1)=5
    I get we mean log base 10

    10^log(3x+1) = 3x+1
    so
    3x+1 = 10^5

    3 x = 10^5 -1 = 9999
    x = 3333

  • Precalculus -

    log(base x)8=-1/2

    x^log(base x)8 = 8
    so
    8 = x^(-1/2) = 1/sqrt x

    sqrt x = 1/8

    x = 1/64

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