Indices and Logarithms

- We use exponents to write very large numbers.

For example, 1000000000 can be written as 10 × 10 × 10 × 10 ×10 × 10 × 10 × 10 × 10 = 10^{9}

It is read as ten raised to the power nine, where 10 is known as base and 9 as the exponent.

The number 10^{9} is known as exponential form of 1000000000.

- If the exponent of a negative base is odd, then the value of the exponential form is negative. However, if the exponent of a negative base is even, then the value of the exponential form is positive.

For example, (−1)^{5} = (−1) × (−1) × (−1) × (−1) × (−1) = −1

(−1)^{6} = (−1) × (−1) × (−1) × (−1) × (−1) × (−1) = 1

- Very large numbers and very small numbers are difficult to read, understand, and compare. To make this easier, we use exponents by converting many of the la…

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