math
posted by Simon on .
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 = e3 then ln(3) = ey
(j) if log(x) = 12 then x = 1.00 x 1012
(k) if ln(x) = 12 then x = 1.00 x 1012
(l) none of these is correct

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 
2 log 10 power 5 +log 10 power 81/2 log 10 power 4 answer