math

Logarithm!!!
Select all of the following that are true statements:
(a) log(2x) = log(2) + log(x)
(b) log(3x) = 3 log(x)
(c) log(12y) = 2 log(2) + log(3y)
(d) log(5y) = log(20y) – log(4)
(e) log(x) = log(5x) – log(5)
(f) ln(25) = 2ln(5)
(g) ln(1) = log(1)
(h) ln(e) = log(10)
(i) if y = e-3 then ln(3) = ey
(j) if log(x) = -12 then x = 1.00 x 10-12
(k) if ln(x) = -12 then x = 1.00 x 10-12
(l) none of these is correct

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  1. type 1 log(xy) = log x + log y

    type 2 log (x)^y = y log x

    now look at a) type 1, true

    b) not type 1, not type 2, false
    in fact log 3x = log 3 + log x

    c) type 1 and type 2
    log (3*2^2* y) = log 3 + 2 log 2 + log y = log 3y + 2 log 2 true

    d) type 1
    log(20y/4) = log(20y) - log(4)

    type 3 base^logbase(x) = x
    g) ln(1) = log(1)
    e^ln 1 = 1 = 10^log 1
    ln 1 = 0 = log 1 true type 3

    h) ln(e) = log(10) ?????????
    e^lne = e so lne =1
    also log 10=1
    so true, type 3

    i) y = e^-3 do not forget the ^ for exponent
    ln y = -3 ln e
    ln y = -3 not what you want

    j) 10^log x = 10^-12
    x = 10^-12 true but remember ^ sign for exponents !

    k) e^ln x = x = e^-12 not 10^-12 false

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  2. 2 log 10 power 5 +log 10 power 8-1/2 log 10 power 4 answer

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