Logatirhms: non-derivatives

Question 1

Basic Inquiry of Logs

Answer 1

log(b3)9
Said as ‘log base three of nine’
3 raised to what power gives us 9?

1. Set a logarithm = x
2. Set left number to the power of the right number = middle number
3. evaluate

Question 2

Solve: log(b10)10000

Answer 2

“10 to the what gives us 10000?”

1. log(b10)10000 = x
2. 10^x = 10000
3. x = 4

Question 3

Solve: log(b2)1/8

Answer 3

“2 to the what gives us 1/8”

1. log(b2)1/8 = x
2. 2^x = 1/8
3. x = -3

For most logarithms, if given a fraction as the middle number, the power will be a fraction

Question 4

Solve: Log(b10) 1

Answer 4

“10 to the what gives us 1”

1. log(b10)1 = x
2. 10^x = 1
3. x = 0

Any number to the 0 power is 1

Question 5

Solve: Log(b10) 0

Answer 5

“10 to the what givers us 0”

1. log(b10)0 = x
2. 10^x = 0
3. no power to a number gives you zero

Question 6

Natural Logs

Answer 6

“A logarithm with ‘e’ as the base”

ln1 = log(b’e’) 1

1. log(b’e’) 1 = x
2. e^x = 1
3. x = 0

Question 7

Solve: ln(e^3)

Answer 7

log(b’e’)’e’^3 = x

1. e^x = e^3
2. x = 3

Question 8

Solve: log(bx)32 = 5

Answer 8

x^5 = 32

x must be 2

Question 9

Solve: log(b5)x = 3

Answer 9

5^3 = x
x = 125

Question 10

Solve: log(b2)7

Answer 10

If not base e or base 10, divide log of big by log of little

log(7)/log(2)

Question 11

Logarithmic Addition Identity

Answer 11

log(b)(xy) = log(b)x + log(b)y

Question 12

Logarithmic Division

Answer 12

log(b)(x/y) = log(b)x - log(b)y

Question 13

Logarithmic Coefficients

Answer 13

log(b)a^n = nlog(b)a