Growth & Decay and log

1a)
5000*(1+0.095)^17
=$23888.9
∴It will grow to $23888.9 at the end of 17 years.

1b)
Let n be the year that the money grow to $18000.
5000*(1+0.095)^n = 18000
(1.095)^n = 3.6
log (1.095)^n = log 3.6
n log (1.095) = log 3.6
n=14.1
∴It takes 15 years for the money grow to $18000.

2a)
log_3 (27) + log_2 (16) - log 100
= log 27/log 3 + log 16/log 2 - log 100
= log (3)^3/log 3 + log (2)^4/log 2 - log 100
=3 log 3/log 3 + 4 log 2/log 2 - 2
=3 + 4 - 2
=5

2015-02-06 16:16:38 補充：
1a) Is $23388.9 not $23888.9

(a) Required amount = 5000(1+9,5%)^17 = $23400 (corr. to 3 sig. fig.)
(b) Let n be the number of year invested.
5000 x (1+9.5%)^n >= 18000
(1.095)^n >= 3.6
n log 1.095>= log 3.6
n>=14.1
Since n is a + integer, so n = 15
It requires 15 years

(a) log 27 (base 3) + log 16 (base 2) - log100
=log 3^3(base3) + log 2^4(base 2) - 2
=3+4-2
=5

2015-02-06 21:01:32 補充：
sorry,
for part b
should use = not >=