Question Chain

Design Intention

Question 1: Given $a^m=M$ , $a^n=N$ , what is ${\log }_{a}M=?$ ${\log }_{a}N=?$

The intention is to introduce the relationship between exponentiation and logarithm and solve simple logarithmic equations.

Question 2: Given $a^m\cdot a^n=a^{m+n}=MN$ , what is ${\log }_{a}MN=?$

Through the analogy of thought, applying the property of exponentiation with the same base, we can derive the property of logarithm with the same base for multiplication.

Question 3: Given $a^m÷a^n=a^{m-n}=\frac{M}{N}$ , what is ${\log }_a\frac{M}{N}=?$

Using the same analogy method as in the previous question, applying the property of exponentiation with the same base for division, we can derive the property of logarithm with the same base for division.