Logarithms:

a)

To understand logarithms, let's start with exponentiation. Exponentiation is a mathematical operation that involves raising a number to a certain power. For example, if we want to calculate 2 raised to the power of 3, we write it as 2^3, which equals 8.

Now, what if we want to find the power (the exponent) to which we need to raise a base number to obtain a specific result? This is where logarithms come in.

a) The logarithm of a number to a given base is the exponent to which the base must be raised to obtain the number. In other words, if we have a base "b" and a number "x", and we want to find the exponent "y" such that b^y = x, then "y" is the logarithm of "x" with base "b", denoted as log base b of x.

For example, let's say we have the base 2 and the number 8. We want to find the exponent "y" such that 2^y = 8. It turns out that 2^3 = 8, so the logarithm of 8 with base 2 is 3. In mathematical notation, we write it as log base 2 of 8 = 3, which means that log2(8) = 3.

To calculate logarithms, you can use a scientific calculator that has a logarithm function built-in. Most calculators will have buttons labeled "log" or "ln," which represent the logarithm with base 10 (common logarithm) and the natural logarithm with base e, respectively. Additionally, some calculators allow you to specify different bases for the logarithm function.

Alternatively, if you don't have access to a calculator, you can use logarithm tables or online logarithm calculators to find the values of logarithms. These tools allow you to input the base and the number for which you want to find the logarithm, and they will provide you with the result.