Express 10 cubed equals 1,000 in its equivalent logarithmic form.
In order to answer this question, we recall that if 𝑎 to the power of 𝑏 is equal to 𝑥, then log base 𝑎 of 𝑥 is equal to 𝑏. The base number 𝑎 in this case is equal to 10. Our exponent or power 𝑏 is equal to three. Our value of 𝑥 is 1,000. This means that the expression could be rewritten as log base 10 of 1,000 is equal to three.
When dealing in base 10, we don’t actually need to write the base. If there is a log button on your calculator, where you don’t need to input the base, this corresponds to base 10. We can therefore simplify our answer such that log of 1,000 equals three.
This rule can be used to convert any expression in exponential form to logarithmic form or vice versa.