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The common logarithm of a number is the exponent you have to raise 1010 by, to get the desired number. For example,

lg(100)=2because102=100. \lg(100)=2 \quad \text{because} \quad 10^2=100.

In the similarity 102=10010^2=100, you could just as easily replace the exponent with lg(100)\lg(100) since this is equal to 2.2. If a logarithm, lg(a),\lg\left(a\right), is an exponent to 1010, you can directly determine the power of ten value by reading of the logarithms argument, a.a.


the Connection between the orders of magnitude and logarithms are common logarithms

Overall, this can be written in the following way.

10lg(a)=a10^{\lg(a)}=a

You can only calculate logarithms of positive numbers. There's no number that you can raise 10 to in order to get zero or a negative result. As a result, this identity applies only when a>0.a > 0.