Precalculus

Solve each exponential equation. Give answers as decimals accurate to the thousands place.

1) log(base5)14=2x-9

2) log(base7)5=7-6x

3) (1/3)^(3x+5)=(9)^(8-x)

4) 4^(x-5)=8^(x+2)

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  1. so did you try?

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  2. i tried 3 and 4 but im not sure if its correct

    3) -21
    4) -16

    and im not sure how to do 1 and 2

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  3. 1) for example:

    log5 (14) = 2x-9

    5^[log5 (14)] = 14 = 5^(2x-9)

    so the question is
    5 to the what = 14 ?
    say 5^z = 14 (we know that z is (2x-9))

    z log 5 = log 14 using base 10 logs (or e or whatever, I use base 10)
    z = log14/log5 = 1.146 / .699 = 1.64
    so
    2x-9 = 1.64
    2x = 10.64
    x = 5.32

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  4. try 3)

    (1/3)^(3x+5)=(9)^(8-x)

    (3x+5) log .333333333 = (8-x) log 9

    (3x+5)(-.4771) = (8-x) (.9542)

    (3x+5) = (x-8) 2 that was lucky :)

    3 x + 5 = 2x-16

    x = -21 agree
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    or this way
    (1/3)^(3x+5)=(9)^(8-x)

    1^(3x+5)/3^(3x+5) = 3^(16-2x)

    1 = 3^(x+21)
    x+21 = 0
    x = -21

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  5. 4) 4^(x-5)=8^(x+2)

    (2^2)^(x-5) = (2^3)^(x+2)

    2^(2x-10) = 2^(3x+6)

    2x-10 = 3x+6

    x = -16 agree

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  6. 2) log(base7)5=7-6x

    5 = 7^(7-6x) = 7^z

    log 5 = z log 7

    z = .827

    7 - 6 x = .827
    6 x = 6.1729
    x = 1.0288

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  7. or, for #1, just change the base to one you know

    log_5(14) = log14/log5 = 1.64
    now you are already at
    2x-9 = 1.64

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