(See attached file for full problem description with proper equations)

---
Logarithms:
a) Using a calculator, find log 10000 where log means log to the base of 10.
Answer:

b) Most calculators have 2 different logs on them: log, which is based 10, and ln, which is based e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer, 0 and 1. When a computer scientist needs a logarithm, he/she needs a log to base 2 which is not on any calculator. To find the log of a number to any base, we can use a conversion formula as shown here:

log_b (a) = log a / log b
Using this formula, find log_2 (1000) .

Apply laws of logarithms to simplify the function. Then find its derivative.
?(x) = ln ^/¯ (9-x2)/(4+x2)
Find
limx→3 2x^4-3x^3-81/x^5-10x^3+27
Apply L'Hopital's rule as many times as necessary, verifying your results after each application

If it takes 9 years for a one-time deposit in a savings account that receives interest compounded quarterly to triple, then what is the interest rate to the nearest tenth of a percent?
To answer this question, you will need to utilize the following relationship:
If ln(x) = N, where N is some number, then x = eN
(if

Use the properties of logarithms to rewrite each expression. Simplify the result if possible.
1. log2 ((2*square root 3)/5)
Given log10 (2) = 0.3010 and log10 (3) = 0.4771, find each logarithm without using a calculator.
2. log10 (20/27)

B) Most calculators have 2 different logs on them: log, which is base 10, and ln, which is base e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer, 0 and 1. When a computer scientist needs a logarithm, he needs a log to base 2 whi

Solve for x finding the exact answer simplified
1b) 2 1n x - 1/3 1n x to the second power = 4
Solve for x (estimate valuses to the thousandths)
2a) 1n x = 5 - 1n 2x
2b) 5 = 7 - 3 e to the -2x power
3) f(x) = 2 + 6 / 1 + e to the kx power
3a) IF f(1)=4 find the value of k
3b) find f(2)
Applied Calculus 9th