Calian wants to construct a viable argument to justify that logbb=1 for b0 and b≠1 . Fill in the blanks to help him construct his argument.(4 points) Any positive number raised to the power is equal to itself. Written as an equation, this means that $$ for any positive base. This equation is equivalent to the logarithmic equation $$. Therefore, it must be true that logbb=1 for any positive base that is not equal to 1.

Question

Calian wants to construct a viable argument to justify that logbb=1 for b>0 and b≠1 . Fill in the blanks to help him construct his argument.(4 points) Any positive number raised to the power is equal to itself. Written as an equation, this means that $$​​​​​​​ for any positive base. This equation is equivalent to the logarithmic equation $$. Therefore, it must be true that logbb=1 for any positive base that is not equal to 1.

GPT-4o mini · Answer

To help Calian construct his argument, we can fill in the blanks as follows:

Any positive number raised to the power 1 is equal to itself. Written as an equation, this means that $$b^1 = b$$ for any positive base b. This equation is equivalent to the logarithmic equation $$\log_b b = 1$$. Therefore, it must be true that log_b b = 1 for any positive base that is not equal to 1.