Logarithimic and exponential equations Flashcards
Exponential form is ?
f ( x ) = a ^ x
a is called ?
x is called?
- The base
- It must be positive
- x is the index or exponent
To undo log…..
To undo log take exponential
To undo exponential…
To undo exponential take log
Log A + Log B
= log AB
( a x b )
Log A - Log B
A
= log _______
B
Log (A) ^n
= n Log A
a = ?
a = a ^ 1
1 = ?
1 = a^ 0
Log a A = ?
Log a A = 1
Log a 1 = ?
Log a 1 = 0
Log a A^ x = ?
Log a A^ x = x
f ( x) = Log 10 x, the inverse ?
f ( x) = Log 10 x, the inverse of f ( x ) = 10
f ( x) = Log e x, the inverse ?
f ( x) = Log 10 x, the inverse of f (x) = e ^ x
Y = ab ^x
Transformed into a graph form
Log y =
log p Y = log p AB ^ x
- ( take Log to the base p of both sides )
log p Y =log p A + log p B ^ x - ( first law of Log )
log p Y = x log p B + Log p A - ( third law of Log)
Y = x log p B + log p A - ( where Y = log p y)
Represent in form Y = mx + c
M =log p B C = log p A
Y = ax ^ b
Transformed into a graph form
Log y =
log p Y = log p AB ^ x
- ( take Log to the base p of both sides )
log p Y =log p A + log p B ^ x - ( first law of Log )
log p Y = x log p B + Log p A - ( third law of Log)
Y = B X + log p A - (where Y = log p y X = log p x)
Represent in form Y = mx + c
M =log p B C = log p A
Straight line equation
Log 10 y = mx + c
M = log p B
C = log p A
Express 5^3 = 125
5^3 = 125
Log 5 125 = 3
Solve Log x 1
- = 2
4
Log x 1
- = 2
4
x^ 2 = 1
-
4
x = 1 1
Square root - = -
4 2
Log 2 1
-
32
Log 2 1
-
32
2^ x = 1 1
— = —- = 2^ -5
32 2^ 5
X = -5
