F3數問題!![log]

a) Let M=10^x and N=10^y where M and N are positive numbers.Then
x=logM and y=logN.


MN=10^x(10^y)
MN=10^(x+y)
x+y=logMN by the definition of log
logMN=x+y
logMN=logM+logN

b) M^n=(10^x)^n
M^n=10^nx
nx=logM^n by the difinition of log
nlogM=logM^n
logM^n=nlogM

c) log(b)x=y
b^y=x
log(a)b^y=log(a)x
ylog(a)b=log(a)x
y=log(a)b / log(a)x
Therefore, log(b)x= log(a)b / log(a)x

if x = 10^a then log x = a
(a) Let x = log(MN)
y = log M
z = log N
10^x = MN ... (1)
10^y = M ... (2)
10^z = N ... (3)
Equate (1) = (2)*(3)
10^x = (10^y)(10^z) = 10^(y + z)
(b) Let x = log(M)
10^x = M
M^N = (10^x)^N
M^N = 10^Nx
log(M^N) = Nx = Nlog(M)
(c) Let y = log(b)x
b^y = x
log(a)b^y = log(a)x
ylog(a)b = log(a)x
y = log(a)x / log(a)b