Calian wants to construct a viable argument to justify that logb b=1

Question

for b>0
and b≠1
. Fill in the blanks to help him construct his argument.(2 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 logb b=1
for any positive base that is not equal to 1.

Answer 1

Here’s how Calian can fill in the blanks in his argument:

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. This equation is equivalent to the logarithmic equation $$ \log_b b = 1 $$. Therefore, it must be true that logb b=1 for any positive base that is not equal to 1.