log₁₆4 = ?

2 

3⁵

243

3⁶

729 

7⁰

1 

(Put into log form)

7776^1/5 = 0

log₇₇₇₆0= 1/5

(Find X)

log₉X = 3/2

X = 27 

log₁₀0.001 = ?

-3 

log₅1/125 = ?

-3 

State the Product Property 

log_b^mn =log_b^m + log_bⁿ

State the Quotient Property 

log_b^m/n = log_b^m - log_b^m 

Find log₃4

log₃(20-5)

log₃20 - log₃5

2.7628 - 1.465  = 1.2978 

State the Power Property 

log_bm^{p =} plog_bm

(Use the Power property to simplify)

log₃3⁷ 

7log₃³

State necessary conditions for exponential growth, in equation y = a• b^x

A must be positive, and b must be greater than 1. 

 State the necessary conditions for exponential decay. 

a must be positive, and b must be greater than 0 and less than 1 

Find exponential function:

(0,3) , (-1,6) 

y = a * b^x

 3 = a * b⁰

a = 3

6 = 3 * b^x

6 = 3b^-1

27^2x = 3^x-2

(3³)^2x = 3^x-2

 ( 6x = x-2 )

x = -2/5 

16²

256 

18³

216 

5^-3

1

____________

5³

3³

27 

3⁴

81 

log₂4 + log₂⁸

2 + 3 =

5 

log₁₀²⁵

log₁₀5 * log₁₀5  =

 .6990 + .6990 =

1.398 

log₃(4x-5) = 5

log_bx = y

b^y = x

3⁵ = 4x-5

243 = 4x-5

248= 4x

62 = x 

log₄x + log₄(x-6) = 2

 (Simplify)

log₄[x(x-6)] = 2 

b^y = x

4² = x(x-6)

(Quadratic) 

log₁₀35 = ?

log₁₀7 * log₁₀5 =

.8451 + .6990 =

1.5441 

log₇1 = ?

0 

Convert into b^y = x format

log₃(1/81) = -4

3^-4 = (1/81)

log₁₀0.0001 = ?

-4 

In calculator terms, "log" is representative of..... 

log₁₀

State the principle behind "Change of Base" 

log_an = log_(b)n / log(b)a

Convert into calculator form:

log₂5

log5

_________

log2 

log₆√5

(Evaluate in terms of common logarithms) 

  log√5

   ______

log6 

=

1/2log√5

____________

log6 

Define logarithm 

A logarithm gives an exponent, or power, to which the base of a number must be multiplied to actually equal the number.

3^-4

1/81

3^x = 11

Solve 

log3^x = log11

_______________

log3

x = log11

      _____

    log3

=  2.186

y = 3 * (1/2)^x

(Growth or Decay?) 

Decay

(b is less than one) 

9^{2n + 1} =27ⁿ

(3²)^{2n + 1 =} (3³)ⁿ

2(2n + 1) = 3n

4n + 2 = 3n

2 = -n

n = -2 

(1/4)³

1/64