2.9 Pre-calculus

Logs to Exponents

100

log₂64=6

2⁶=64

200

log₄1/64=-3

4^-3=1/64

300

log₂₅125=3/2

25^3/2=125

400

log₂8=3

2³=8

500

log₂36=2

6²=36

Exponents to logs

100

10³=1000

log1000=3

200

16^5/2=1024

log₁₆1024=5/2

300

10^-2=1/100

log1/100=-2

400

13²=169

log₁₃169=2

500

9^-2=1/81

log₉1/81=-2

Value of logarithm(no calculator)

100

log₅625

log₅625=x

5^x=625

5^x=5⁴

x=4

200

log100000

log100000=x

10^x=100000

10^x=10⁵

x=5

300

log₂₇81

log₂₇81=x

27^x=81

3^3x=3⁴

3x=4

x=4/3

400

log₂16

x=4

500

log₅x=3

5³=x

x=125

Value of logarithm(With calculator)

100

log140

2.146

200

log₉120

2.179

300

log₃18

2.631

400

log39

1.591

500

log₄25

2.322

Facts about logs

100

The formula for logarithmic functions 

log_bC=A

200

The formula for exponential functions

B^a=C

300

Logs are the inverse of 

exponential functions 

400

The year logs were invented 

1614

500

True or False

Negative bases are allowed in logarithmic functions 

False

Negative bases are not allowed in logarithmic functions