Math 41 Sections 6.6, 6.7, and 6.8

# Math 41 Sections 6.6, 6.7, and 6.8 - Math 41 6.6...

• Notes
• 9
• 100% (1) 1 out of 1 people found this document helpful

This preview shows pages 1–4. Sign up to view the full content.

Math 41 6.6 Logarithmic and Exponential Functions - y = log a x is equivalent to x = a y a > 0, a ≠ 1 - If log a M = log a N, then M = N. M,N, and a are positive and a ≠ 1. Example 1: Solving a Logarithmic Function Solve: 2 log 5 x = log 5 9 Solution: The domain of the variable in this equation is x > 0. Because each logarithm is to the same base, 5, we can obtain an exact solution as follows. 2 log 5 x = log 5 9 Log 5 x 2 = log 5 9 X 2 = 9 X = 3 Can’t be -3 since x > 0. Example 2: Solving a Logarithmic Function Solve: ln x + ln(x – 4) = ln(x + 6) Solution: The domain of the variable requires that x > 0, x – 4 > 0 and x + 6 > 0. As a result, the domain of the variable here is x > 4. We begin the solution using the log of a product property. Ln x + ln(x – 4) = ln(x + 6) Ln[x(x – 4)] = ln(x + 6) X(x – 4) = (x + 6) X 2 – 4x = x + 6 X 2 – 5x – 6 = 0 (x – 6)(x + 1) = 0 X = 6 or x = -1 Can’t be -1 since x > 4. - If a u = a v , then u = v a > 0, a ≠ 1 Example 3: Solving an Exponential Function Solve: 2 x = 5 Solution: Since 5 cannot be written as an integral power of 2, we write the exponential equation as the equivalent logarithmic equation. 2 x = 5

This preview has intentionally blurred sections. Sign up to view the full version.

Math 41 X = log x 5 X = ln5 / ln2 Change of base = 2.322
Math 41 6.7 Compound Interest - the total amount borrowed from a bank, person, etc is known as the principal. The rate of interest , expressed as a percent, is the amount charged for the use of the principal for a given period of time. Simple Interest Formula I = Prt - When the interest due at the end of a payment period is added to the principal so that the interest computed at the end of the next payment period is based on this new principal amount, the interest is said to have been compounded . Compound interest is interest paid on principal and previously earned interest. Example 1: Computing Compound Interest A credit union pays interest of 8% per annum compounded quarterly on a certain savings plan. If \$1000 is deposited in such a plan and the interest is left to accumulate, how much is in the account after 1 year? Solution: I = Prt I = (1000)(.08)(1/4) = \$20 The new principal is 1020. At the end of the second quarter, the interest earned is I = (1020)(.08)(1/4) = \$20.40 The new principle is 1040.40.

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.
• Fall '07
• BRUNSDEN,VICTORW

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern