# Logarithimic and exponential equations Flashcards

1
Q

Exponential form is ?

A

f ( x ) = a ^ x

2
Q

a is called ?

x is called?

A
• The base
• It must be positive
• x is the index or exponent
3
Q

To undo log…..

A

To undo log take exponential

4
Q

To undo exponential…

A

To undo exponential take log

5
Q

Log A + Log B

A

= log AB

( a x b )

6
Q

Log A - Log B

A

A
= log _______

`               B`
7
Q

Log (A) ^n

A

= n Log A

8
Q

a = ?

A

a = a ^ 1

9
Q

1 = ?

A

1 = a^ 0

10
Q

Log a A = ?

A

Log a A = 1

11
Q

Log a 1 = ?

A

Log a 1 = 0

12
Q

Log a A^ x = ?

A

Log a A^ x = x

13
Q

f ( x) = Log 10 x, the inverse ?

A

f ( x) = Log 10 x, the inverse of f ( x ) = 10

14
Q

f ( x) = Log e x, the inverse ?

A

f ( x) = Log 10 x, the inverse of f (x) = e ^ x

15
Q

Y = ab ^x

Transformed into a graph form

A

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

16
Q

Y = ax ^ b

Transformed into a graph form

A

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

17
Q

Straight line equation

A

Log 10 y = mx + c

M = log p B

C = log p A

18
Q

Express 5^3 = 125

A

5^3 = 125

Log 5 125 = 3

19
Q

Solve Log x 1
- = 2
4

A

Log x 1
- = 2
4

x^ 2 = 1
-
4

x = 1 1
Square root - = -
4 2

20
Q

Log 2 1
-
32

A

Log 2 1
-
32

2^ x = 1 1
— = —- = 2^ -5
32 2^ 5

X = -5