Name:__________ warm-up 7-3

Solve 42x = 163x – 1 Solve 8x – 1 = 2x + 9

Solve 52x – 7< 125 Solve

A money market account pays 5.3% interest compounded quarterly. What will be the balance in the account after 5 years if $12,000 is invested

Charlie borrowed $125,000 for his small business at a rate of 3.9% compounded annually for 30 years. At the end of the loan, how much will he have actually paid for the loan?

Details of the DayEQ: How do radical functions model real-world problems and their solutions?

How are expressions involving radicals and exponents related?

I will be able to…

Activities:Warm-upReview homeworkNotes: 7-3 Logarithmic and Logarithmic functionsClass work/ HW

Vocabulary:•logarithmic function•logarithm•http://www.purplemath.com/modules/logs.htm

.

.• Evaluate logarithmic

expressions.

• Graph logarithmic functions.

7-3 Logarithm and Logarithmic Functions

A Quick Review Solve 42x = 163x – 1 Solve 8x – 1 = 2x + 9

Solve 52x – 7< 125 Solve

A Quick Review A money market account pays 5.3% interest compounded quarterly. What will be the balance in the account after 5 years if $12,000 is invested

Charlie borrowed $125,000 for his small business at a rate of 3.9% compounded annually for 30 years. At the end of the loan, how much will he have actually paid for the loan?

Notes and examples

Write log3 9 = 2 in exponential form.

B. Write in

exponential form.

Notes and examplesWhat is log2 8 = 3 written in exponential form?

What is 34 = 81 written in logarithmic form?

What is –2 written in exponential form?

B. Write in

logarithmic form.

Notes and examplesWhat is written in logarithmic form? Evaluate log3 243

Evaluate log10 1000

Notes and examples

Notes and examplesGraph the function f(x) = log3 x

Graph the function

Notes and examplesGraph the function f(x) = log5x Graph the function

Notes and examples

● : The graph is compressed vertically.

● h = 0: There is no horizontal shift.

● k = –1: The graph is translated 1 unit down.

Notes and examples● |a| = 4: The graph is stretched vertically.

● h = –2: The graph is translated 2 units to the left.

● k = 0: There is no vertical shift.

Notes and examples

Notes and examplesA. AIR PRESSURE At Earth’s surface, the air pressure is defined as 1 atmosphere. Pressure decreases by about 20% for each mile of altitude. Atmospheric pressure can be modeled by P = 0.8x, where x measures altitude in miles. Find the atmospheric pressure in atmospheres at an altitude of 8 miles.

Notes and examplesB. AIR PRESSURE At Earth’s surface, the air pressure is defined as 1 atmosphere. Pressure decreases by about 20% for each mile of altitude. Atmospheric pressure can be modeled by P = 0.8x, where x measures altitude in miles. Write an equation for the inverse of the function.

Notes and examplesA. AIR PRESSURE The air pressure of a car tire is 44 lbs/in2. The pressure decreases gradually by about 1% for each trip of 50 miles driven. The air pressure can be modeled by P = 44(0.99x), where x measures the number of 50-mile trips. Find the air pressure in pounds per square inch after driving 350 miles.

Notes and examplesB. AIR PRESSURE The air pressure of a car tire is 44 lbs/in2. The pressure decreases gradually by about 1% for each trip of 50 miles driven. The air pressure can be modeled by P = 44(0.99x), where x measures the number of 50-mile trips. Write an equation for the inverse of the function.