if $5,000 is invested at an interest rate of 5% per year ... › cms › lib02 › sc01001931 ›...

If $5,000 is invested at an interest rate of 5% per year, find

the amount of the investment at the end of 5 years for the

following compounding methods:

Annually

Monthly

Quarterly

Continuously

Logarithmic Functions

Section 6.3

Logarithms

Used to find unknown exponents in

exponential models

Define many measurement scales in the

sciences such as the pH, decibel, and Richter

scales.

Logarithmic Function

It’s the inverse of the exponential function

log ya x y a x

Graph: 2( ) logf x x

Domain:

Range:

Graph: 2( ) 3 logf x x

Domain:

Range:

Graph: 2( ) log ( 4)f x x

Domain:

Range:

Graph: 2( ) log ( 2)f x x

Domain:

Range:

For any positive base b, where b≠1:

bx = y if and only if x = logby

Exponential Form Logarithmic Form

310 1000 10log 1000 3

Write in logarithmic form.

35 125

Write in logarithmic form.

46 1296

Write in logarithmic form.

3 13

27

Natural log

log lne x x

Write in logarithmic form.

2 7.389...e

Write in exponential form.

3log 81 4

Write in exponential form.

8log 512 3

Write in exponential form.

ln(181.3) 5.2

Write in exponential form.

3

1log 2

9

Find the value of x.

4log 64x

Find the value of x.

2log 16x

Find the value of x.

125log 5x

Find the value of x.

5 log 32x

Find the value of x.

34 log x

Find the value of x.

2log 1x

Find the value of x.

1log 9

2x

Find the value of x.

73 log x

Find the value of x.

9log 3x

Find the value of x.

1ln x

e

Solve

( ) ln 44f x x for x

Find to the nearest thousandth – using the calculator.

10( ) log 240f x x for x

Find to the nearest thousandth – using the calculator.

10 85x

Find to the nearest thousandth – using the calculator.

10 22x

Homework

Worksheet