Logarithms and Exponentials Review

Evaluating Logs

100

Evaluate: log₃81=

4

200

Evaluate: log₄(1/16)=

-2

300

Evaluate (round to 3 decimal places): log567=

2.754

400

Evaluate (round to 3 decimal places):  log₅422=

3.756

500

Evaluate (round to 3 decimal places): log₇₀5=

0.379

Solve Exponentials

100

Solve: 7^x=343

x=3

200

Solve: 6^x+5= 125

(round to 3 decimal places)

x=2.672

300

Solve: 3(5)^x=660

(round to 3 decimal places)

x=3.351

400

Solve: 2(13)^x-2=18

(round to 3 decimal places)

x=0.898

500

Solve: (1/2)^x-4=30

(round to 3 decimal places)

x=-5.087

Writing Exponentials

100

Write the equation: There are 8 ants and they double in number every week.

y=8(2)^x

200

Write the equation: There are 40 spiders in a shed. A bug exterminator sprays the spiders. They amount of spiders decreases by 1/2 each hour.

y=40(1/2)^x

300

Write the equation: There are 10 dandelions in a field. They triple in number 5 times a week.

y=10(3)^5x

400

Write the equation: You deposit $15 in an account that earns 2% interest once a month.

y=15(1.02)^x

500

Write the equation: There are 5 feet of snow on the side of the mountain. In the spring, 20% of the snow melts once every 3 weeks.

y=5(.80)^x/3

Solving Logarithms

100

Solve: log₃x=2

x=9

200

Solve: log₅x=-3

x= 1/125

or x=0.008

300

Solve: logx+8=12

x=10000

400

Solve: 2log₇x=5

x=129.642

500

Solve: log_3.4(x+2)=7

x=5250.335