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#461 / Math Easy

Solve the shown logarithm:

Expand 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,

$$$log_9(9^4)=4$$$

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