What+is+a+Logarithm

If I were to ask you to perform the following calculation.

2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 Rather than going through your 2 times table in your head (2,4,6,8... and so on) you might observe that there are ten twos and so simply think of this as.

2 x 10 You are probably familiar with the idea that we can think of multiplication as repeated addition. So what about repeated multiplication.

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 Instead of writing the above we would normally write.

210 We call the 10 the **exponent** or **power** and would say we have raised two to the power of 10.

Let us go back to our multiplication example, you know that 2 x 10 = 20.

The reverse process of multiplication is division and so 20 ÷ 2 = 10. Similarly there is a reverse function to go with **exponents.** We call it the **logarithm.**

2 10 is 1024, and so log 2 1024 = 10. The 2 in this case is what we call **the base.**

If we take the log of a value (to the base of 2), we find the exponent or power of 2 which is equal to this value.

More generally

If y = ab

Then logay = b

It is important that we specify the base to which we are taking the logarithm, for example:

34 = 81 but 92 = 81 also

So log381 = 4 but log981 = 2

So the value of the **logarithm** depends on the **base.**

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