Chapter 3 logs

Expand/Condense

100

Expand: written on Smart Board

1/4 log a - 2log b

200

Condense: 1/3log a + 2log (b+1)

log a^1/3(b+1)²

300

Expand: log 5x⁴y² / z³

log 5 + 4log x + 2log y - 5log z

400

Condense: 8lnx + 1/2lny + 5lnz - ln9

ln x⁸y^1/2z⁵ /9

500

Expand: ln ex²/(y³z)

1+ 2lnx - 3lny - lnz

Concepts

100

What are the implied bases for logx and lnx?

logx: 10 and lnx: e

200

log₅ 1 =

0

300

ln (-10) =

undefined

400

ln e = 

1

500

log 10 = 

1

Solve

100

log₇ 15x + log -13 = 6

invalid

200

ln x + ln 7 = ln (x + 12)

x = 2

300

log₅ (x² + 4) = 3

+11, -11

400

2log₂ (x - 9) = 18

521

500

log₄ (x - 3) - log₄ 9 = 1

x = 39

Word Problems

100

Suppose $6,500 is put into an account that pays an annual rate of 4% compounded weekly. How much will be in the account after 40 years?

$32,174.90

200

Suppose $9,500 is put into an account that pays an annual rate of 2% compounded continuously. How much will be in the account after 20 years?

$14,172.30

300

Suppose $15,000 is put into an account that pays an annual rate of 6.99% compounded quarterly. How much will be in the account after 18 years?

$52,215.70

400

Find the rate at which the population of elephants is declining if there were 682 in the beginning and only 254 after 13 years.

7.3%

500

Find the rate at which the population of spotted lantern flies is increasing if there were 300 in the beginning and 986 after 5 years

26.9%

Solve

100

ln x = -5

0.0067

200

log₆ (1/36)

-2

300

e^x+4 = 63

0.14

400

5^3x = 25^x+1

x = 2

500

log(-6x + 2) = log(x² +10)

x = -2, -4