Calian wants to construct a viable argument to justify that

Question

log
b
b
=
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
log
b
b
=
1
for any positive base that is not equal to 1.

Answer 1

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. 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.