Logarithm!!!

Question

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

Answer 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

Answer 2

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