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