Log
Solve the shown logarithm:
Hint
The logarithm of
$$x$$
to the Base
$$b$$
is defined by
$$$log_b(x)=c$$$
where
$$b^c=x$$
.
Hint 2
Factor 9 from 6,561.
The logarithm of
$$x$$
to the Base
$$b$$
is defined by
$$$log_b(x)=c$$$
where
$$b^c=x$$
.
The problem is asking to solve for
$$c$$
:
$$$9^c=6,561$$$
Factor
$$9$$
from
$$6,561$$
:
$$$\frac{6,561}{9}=729\rightarrow \frac{729}{9}=81\rightarrow \frac{81}{9}=9$$$
$$9$$
evenly appears four times in
$$6,561$$
. Thus,
$$$log_9(9^4)=4$$$
4