Exponential and Logarithmic Functions!

Rewriting Logarithmic and Exponential Functions

100

Write this function as an exponential function

log₄x=12

4¹²=x

200

Write as an exponential function

4³=64

log₄64=3

300

Write in logarithmic form

6^-2 = 1/36

log₆1/36 = -2

400

write as an exponential function

ln(x - 1) + 1 = 3

e²=(x - 1)

or 

e² +1 = x

Expanding/Condesning

100

Expand

ln3x

ln3  *  lnx

200

Condense  2logx - log5

log (x²/5)

300

Condense   log₄g - 3log₄h

log  (g/h³)

400

Expand    log(x²y³/z⁴)

2logx + 3logy - 4logz

500

Condense   (1/2)Lnx + 2Lny - 3Ln(x+3)

Ln (x^1/2y² / (x+3)³)

Solving

100

Solve for x 

log₅x = 3

125

200

Solve for x

5^x-2 - 15 = 10

x = 4

300

Solve and round to 3 decimal places

8^3x = 360

x = 0.944

400

Solve for x and round to 3 decimal places

250e^0.02x = 10,000

x = 184.444

500

Solve for x and round to 3 decimal places

5(2^3-x) - 13=100

x = -1.498

RANDOM LOG INFO

100

What is the base of a common log?

10

200

what is the NATURAL base?

e

300

What is the true name of "e" and write it to 3 decimal places. 

Euler's Number

2.718

400

What is the change of base formula?

Rewrite log₃14 using the change of base formula. DO NOT SOLVE!

log14/log3

500

Mr. Kingston wants to open a bank account. He has chosen the option of 7% interest compounded semiannually (n=2 ).  Kingston wants to save 100,000 NT and would like to do it in 10 years. How much money should he put in the account to start? Round your answer appropriately.

A=P(1+r/n)^nt

about 50,257 NTD

Miscelaneous

100

How many siblings does Mr. Hermanson have?

2

200

How many oceans are there in the world?

5

300

At what temperature is Fahrenheit and Celsius the exact same?

- 40 degrees

400

Name all 7 continents in the world

Asia, Africa, North America, South America, Antarctica, Europe, Australiia

500

Written language was invited by who?

4 possible answers

Egyptians, Sumerians, Chinese, Mayans