A. Convert to logarithmic equations. For example, the logarithmic form of "23 = 8" is "log2 8 = 3".

a) 16 3/2 = 64

b) ex = 5

B. Write the logarithmic equation in exponential form. For example, the exponential form of "log5 25 = 2" is "52 = 25".

a) log 3 27 = 3

b) log e 1 = 0

c) log 125 25 = 2/3

C. Use the properties of logarithmic functions to expand the following logarithmic expressions

a) log10 4x2y

b) log a [(7x + 4)1/2 / 3]

D. Express the following as a single logarithm.

a) ½ log 10 x + 2 log 10 ( x - 2)

b) 4 log 10 (x - 3) - log 10 x

E. Solve the following for x:

a) 4(2x) = 56

b) ex = 66

c) ex - 5 = 41

d) log10 5x + log10 (x + 1) = 2

e) 2 log5 9x = 6

F. When interest is compounded continuously, the balance in an account after t years is given by A = Pert,
Where P is the initial investment and r is the interest rate.
Use the formula given to solve the following:

a) Maya has deposited $600 in an account that pays 5.64% interest, compounded continuously. How long will it take for her money to double?
b) Suppose that $2000 is invested at a rate of 6% per year compounded continuously. What is the balance after 1 yr? After 2 yrs?

Solution Summary

Exponential and logarithmic functions are fully investigated in the attached Word document.

1. Convert the following equations into logarithmic form: a. 2 = 6x. b. 7 = 6y. ... d. X = 8y. 2. Convert the following equations into exponential form: ...

... For questions 1-2, convert to logarithmic equations ... For example, the logarithmic form of "23 = 8" is ... W6A1 #1 Do exponential functions only model phenomena that ...

... Logarithms can also be converted between any ... any explicit use of the exponential notation; this ... are required for calculating logarithmic functions of smaller ...

... 2. We use the word problem and convert it to ... Example: exponential: {1, 3, 9, 27, 81, 243, 729, 2187 ... is square root (just like the inverse of log is exponent). ...

... be converted easily into a statement about odds ratio of the dependent rather than log odds simply by using the exponential function (raising the natural log e ...

... the radical symbol is widely used, converting to rational ... in decibels using a logarithmic scale and is ... linear, quadratic, rational, or exponential) is related ...