Problem 695

Evaluate the expression: log100

Solution:-

log 100

log = 2 log 10

we know log 10 = 1

log 100 = 2(1) = 2

Exponential Expression

Exponential Expression

If a is a real number and n is a natural number,

an  =  a .a .a ……a,

n factors of a

where n is the exponent, a is the base, and an is an exponential expression.

Exponents are also called powers.

For example, the product  2 . 2 . 2 . 2 . 2  is written

2 . 2 . 2 . 2 . 2 = 25.

5 factors of 2

The number 5 shows that 2 is used as a factor 5 times. The number 5 is the

exponent, and 2 is the base.

25   Exponent

Finding root a^2

Finding

In the expression , the radicand is a perfect square. It is tempting to think

that = a, but we see below that this is not the case.

Suppose a = 5. Then we have , which is  , or 5.

Suppose a = -5. Then we have ,which is  , or 5.

Suppose a = 0  . Then we have which is  , or 0.

The symbol never represents a negative number. It represents the

principal square root of  a2. Note the following.

SIMPLIFYING

a ≥ 0 = a

if a is positive or 0 ,the principal square root of is a.

a < 0 = -a

If a is negative, the principal square root of is the opposite of a.

In all cases, the radical expression represents the absolute value of a.

PRINCIPAL SQUARE ROOT OF a2

For any real number a, =  \left | a \right | . The principal (nonnegative) square

root of a2 is the absolute value of a.