Comparison method of exponential function in senior one mathematics.

This is mainly to find a special value to compare, and generally choose 1 as the comparison item.

take for example

Compare the size of 1.2 to the 0.7 power and 1. 1 to the 0.8 power.

first

Cardinal number 0.7 is greater than 0 and less than 1, which is a decreasing function.

Cardinality 1. 1 is greater than 1, which is an increasing function.

Then look at the 0.7 power of 1.2 and compare it with the 0.7 power.

The exponent 1.2 is greater than the exponent 0, but it is a decreasing function, so the power of the whole 0.7 1.2 is less than the power of 0.7, that is, less than 1.

Let's look at the 0.8 power of 1. 1. Similarly, the power of 1. 1 is equal to 1.

Exponent 0.8 is greater than exponent 0, which is an increasing function, so the 0.8 power of integer 1. 1 is greater than the 0 power of 1. 1, that is, it is greater than 1.

Then it is clear that a result less than 1 and a result greater than 1 come out.