Question

1.)An initial investment of $10,000 grows at 11% per year.What function represents the value of the investment after t years?
2.)Evaluate log 0.01 by using mental math?

Answer 1

1) The value of an investment is
TOTAL = principal*(1+ rate)^t where t = years
TOTAL = 10,000 * (1.11)^years

2) I'm assuming it is a base 10 log.
So, whenever a base 10 log is to be found, if the number is exactly a power of 10, (.1, 1 , 10 , 100, 1,000) then the log is the exponent of that number
.1 = -1,
1 = 0
10= 1
100= 2
1,000 = 3

So, the base 10 log of .01 is -2, because 10^-2 = .01

Answer 2

ok thankyou! Could you also help me with this problem please?
\[\log_{6} x ^{8}-\log_{6} x ^{5}=31\]

Answer 3

Well at least I can give it a try.

Answer 4

(log 10) x^8 - (log 10) x^5 = y
If x=10, then 8 -5 =3
then y = 3
Well that's with base 10 logs and knowing the value of x.
That's about all I can do.

Answer 5

\[\Large \log_{6}(x^8)-\log_{6}(x^5) = 31\]


\[\Large 8\log_{6}(x)-5\log_{6}(x) = 31\]


\[\Large (8-5)\log_{6}(x) = 31\]


\[\Large 3\log_{6}(x) = 31\]


\[\Large \log_{6}(x) = \frac{31}{3}\]


\[\Large x = 6^{31/3}\]

Answer 6

okay! Thanks !!!

Answer 7

Very good Jim!!

Answer 8

Do you guys know any good example websites for Math ?

Answer 9

here is one page that shows various log rules

http://www.purplemath.com/modules/logrules.htm

Answer 10

thankyou! (:

Answer 11

np

Answer 12

Mhm120
My own site www.1728.org has lots of math examples and calculators.
Not too much on logs but here is a great log calculator
http://1728.org/logrithm.htm

Answer 13

Incidentally Jim I tested out your answer
109,874,333.58 (or 6^31/3)
and the log 6 of that number to the 8th power - the log 6 of that number to the 5th power
= 31

Answer 14

@jim_thompson5910 Could you please what you did for the log problem in words please?