對數及根式

若3^a = 9^b = 10^c,且a, b, c不為0,則c/b - c/a =
A. log1/3
B. 1
C. 3
D. log3

3^a = 9^b = 10^c
log(3^a) = log(9^b) = log(10^c)
a(log3) = b(log9) = c(log10)
a(log3) = b[log(3^2)] = c
a(log3) = 2b(log3) = c

a(log3) = 2b(log3)
a = 2b ... (1)

c = 2b(log3) ... (2)

Put (1) and (2) into (c/b) - (c/a) :
(c/b) - (c/a)
= c[(1/b) - (1/a)]
= 2b(log3)[(1/b) - (1/2b)]
= 2b(log3)(1/2b)
= log3


若log10(x) + log10(3) =log10(x + 3),x的值是什麼?
A. 0
B. 1
C. 3/2
D. x,可能是任何正數

log10(x) + log10(3) =log10(x + 3)
log10(3x) =log10(x + 3)
3x = x + 3
2x = 3
x = 3/2