Logarithm
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 25 from 15,625.
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
$$c$$
:
$$$36^c=15,625$$$
Factor
$$25$$
from
$$15,625$$
:
$$$\frac{15,625}{25}=625\rightarrow \frac{625}{25}=25$$$
$$25$$
evenly appears three times in
$$15,625$$
. Thus,
$$$log_{25}(25^3)=3$$$
3