Logirthms Please could you please help me

2. Fill in the blank: ln e^3 = _____.







9. Solve the following equation for x:

logx +log(x-1) = log(4x)

(Points : 2)
x = 5

x = 0,5 <----- I think it is this one!

x = 1/4log(x - 1)

There are no solutions.



8. If log(M/N)=5 and log(P/N)=7, what can you say about the relationship between M and P?
(Points : 2)
P = 2M

P = 10M

P = 100M

M = 2P

ln e^3 = 3

logx +log(x-1) = log(4x)
log[x(x-1)] = log(4x)
x(x-1)=4x
x-1=4
x=5

log(P/N)=7
log(M/N)=5
log(P/N)-log(M/N)=7-5
log(P/M)=2
P/M=10²
P=100M

2) It appears that you donot know the meaning of ln ; ln stands for Natural logarithm
Let ln e^3 = x , (base of Natural logarithm is e, i.e. ln -------- = log(e) -------- )
=> e^x = e^3 ( according to the definition of logarithm)
=> x = 3
=> ln e^3 = 3
9) You are correct
log x + log (x-1) = log (4x)
=> log {x(x - 1)} = log (4x)
=> x(x - 1) = 4x
=> x² - x = 4x
=> x² - 5x = 0
=> x(x - 5) = 0
=> x = 0 or 5
8) log stands for common logarithm in which the base is 10, i.e. log ------- = log(10) ---------
log (M / N) = 5
=> log M - log N = 5 .......... (1)
log (P / N) = 7
=> log P - log N = 7 ........... (2)
Subtracting (1) from (2) we get
log P - log M = 2
=> log (P / M) = 2
=> P / M = 10² = 100
=> P = 100 M (Option 3)
Remember the difference between ln and log

2> ln e^3 =3lne =3
9> logx(x-1)=log4x
=> x(x-1)=4x
=> x=0 or x=5
8> m/n=10^5
p/n=10^7
p/m=100
p=100m