LOGS

Information

100

What is a Logarithm

A higher number represented by a base and exponent

200

What is log_0?

Undefined

300

What base is log standard?

log₁₀

400

What is log_e

ln

500

Who invented Logarithms?

John Napier

Easy Problems

100

Write the exponent in logarithmic form:

3⁵=243

log₃(243)=5

200

Write the exponent in logarithmic form:

5²=25

log₅(25)=2

300

log(1)

0

400

Solve log₄(16)

2

500

Solve log₂₈

1.45

Somewhat easy Problems

100

If log₂(x)=2, solve for x

x= 4² or 16

200

log₂(x)=2

x=4

300

log₂(x)+log₂(x-2)=3

x=4

400

(3)^2-x = 243

x=-3

500

log₉(9)

1

Difficult (not just solving)

100

Simplify;

log(x) + log(y)-log(2)

log(xy/2)

200

If log₂(y/3)=4, solve for y

y=48

300

Use inverses to write in exponentiation;

log_x8=3

x³ = 8

400

What kind of operation is a logarithm? (Hint: how it relates to other operations)

The inverse operation to exponentation/raised power

500

Solve;

log₆(x+9) + log₆(x) = 2

3=x

{x=-12 is an extraneous answer}

It's a mix

100

Convert M^x=N to Logarithmic form

log_m(N)=M

200

What does the 2 represent in this equation?

2³=8

the base

300

How much more energy is released on a magnitude 4.0 earthquake as compared to a magnitude 3.0 earthquake?

(Note; Richter scale is logarithmic.)

10x more energy

400

Evaluate; Round to the nearest thousandth:

log₇18

1.485

500

log₄₉7 – log₈4

3/4