**Log x is undefined at x equal to 0** : If **x= 10 power y**, 10 power y greater than zero, this implies that **x greater than zero**. This means that **log x exist only when x greater than zero**. This implies that the **Domain of the log x is a positive real number.**

**Log x is undefined at x equal to 0 image:**

**Resultant Note:**

**log x is undefined at x=0**

For the graph of** y=** **f(x) = log x,** we fined the value of log x from the c**ommon Logarithm** table for** various values of x greater than zero**.

**Values of Log x**

**Log of zero **

** (1)** Log (0)= – ∞

**Log of 0.1**

(2) Log (0.1) = -1

**log of 1**

**(3)** Log(1) =0 where x always values greater than zero.

**Log of 2**

**(4)** Log (2) = 0.30

**Log of 4**

**(5)** Log(4) = 0.60

**A table** of some of the** corresponding values of x and f(x)** is shown.

x |
→0 |
o.1 |
1 |
2 |
4 |
6 |
8 |
10 |
→ +∞ |

y=f(x)= Log |
→-∞ |
– 1 |
0 |
0.30 |
0.60 |
0.77 |
0.90 |
1 |
→ +∞ |

**Values of Exponential Function:**

**As the approximate value of “e” is 2.718**

the graph of **“e power x”** has the same characteristic and the properties of **“a power x”when a > 1**

**Exponential power zero**

**Exponential power one**

**Exponential power two**

**Exponential power -1**

**Exponential power -2**

**Exponential power -3**

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**log rule exponential of real number****logarithm laws of real number****Mantissa of logarithm of real number****Finding common logarithm of any number**