Logs and Exponents

Question 1

How to find number of years in exponential growth.

Answer 1

Get percentage of growth, times by it each time until you get answer or level of growth, then explain.

Question 2

Show 5^3 = 125 in logarithmic form

Answer 2

log (base5) 125 = 3

Question 3

Evaluate log (base 4) 16

Answer 3

4 to power of y = 16, y must be two, therefore log (base 4) 16 = 2. You find power required to get number.

Question 4

3 Laws of Logarithms

Answer 4

Adding logs with the same base means times.
Subtracting logs with same base means dividing.
The power of a log ‘flies’ to the front and vice versa.

Question 5

What happens with log of the same base and number, such as log(7)7

Answer 5

Same base and same number means the answer is 1.

Question 6

How do you get rid of a log in an equation?

Answer 6

Take the exponent on both sides.

Question 7

What do you do when dealing with constants (numbers) in an logarithmic equation?

Answer 7

Write constants as logs, such as + 3 being 3 x log(base2)2 since log(base2)2 = 1.

Question 8

How to get rid of exponents in equations?

Answer 8

Take natural log of both sides (ln)

Question 9

How to deal with exponential growth and decay

Answer 9

For initial mass, make t=0, for half life, replace the G with half the mass etc. Work like that, take exponents and natural logs etc.

Question 10

Graphing Logarithmic Data

Answer 10

Expand to make in form y=mx+c, and work by finding values and subbing in points to get values of letters, then rewrite.