# Math 111 Final Exam Review

## Chapter 5

### 5.1: Radicals and Rational Exponents

You should have your exponent laws imprinted in your gray matter. You should
be comfortable with

reducing radical and exponential expressions.

41. Simplify the expression

42. True/False?

### 5.2: Exponential Equations and 5.2A: Compound Interest and the numbere

You need to be comfortable working with exponential equations. You need to be
able to set up

exponential equations from word problems. You need to be able to solve for
variables in the exponent

using logarithms. You should know the formulas for compound interest.

Problems from 5.2: 19-23, 51-62, 64-76.

Problems from 5.2A: 1-29.

43. Hercules ate 7 grams of Uranium, and now he is sprouting eyes at an
exponential rate. He had two eyes

when he ate the Uranium. 3 hours later, Hercules has 14 eyes. Find an
exponential function whose

input is the number of hours since Hercules ingested Uranium, and the output is
the number of eyes

Hercules has. How many eyes will Hercules have after 24 hours? When will
Hercules have 5000 eyes?

Give an exact answer and decimal approximation.

44. Recall the formula for continuous compounding is f(t) = Pe^{rt}. You invest
500$ in an account with

7.5% interest, compounded continuously. How much will be in your account after 5
years? How long

will it take for your account to double? Give an exact answer and decimal
approximation.

### 5.3: Common and Natural Logarithms

You should know the properties of Logarithms in general. Namely, they are the
inverse functions to

exponential functions, their domain and range...all the information in the box
on p. 365.

Problems from 5.3: 1-36, 43-46, 84

### 5.4: Properties of Logarithms and 5.4A: Logarithmic Functions to Other Bases.

You need to be very comfortable with the Product Law, Quotient Law, and Power
Law. These are the

main tools for working with logarithms. You should be able to write sums and
differences of logarithms

as a single logarithm.

Problems from 5.4: 1-31.

Problems from 5.4A: 1-60, 69 - 74

45. True/False.

for a, b > 0, a≠b.

46. Write the following as a single logarithm.

### 5.5:Algebraic Solutions of Exponential and Logarithmic Equations

You should be able to solve exponential and logarithmic
equations algebraically. Don’t forget to check

your answers when solving logarithmic equations.

Problems from 5.5: 1-29, 35- 80.

47. Solve the following equation:

48. Solve the following equation:

49. Solve the following equation.