## Base Log

Solve the shown logarithm:

##
__
__**Hint**

**Hint**

The logarithm of
$$x$$
to the Base
$$b$$
is defined by

$$$log_b(x)=c$$$

where
$$b^c=x$$
.

##
__
__**Hint 2**

**Hint 2**

Special definitions when
$$b=e$$
or
$$b=10$$
are:

- ln $$x$$ → Base = $$e$$
- log $$x$$ → Base = 10

The logarithm of
$$x$$
to the Base
$$b$$
is defined by

$$$log_b(x)=c$$$

where
$$b^c=x$$
. Special definitions when
$$b=e$$
or
$$b=10$$
are:

- ln $$x$$ → Base = $$e$$
- log $$x$$ → Base = 10

The problem is asking to solve for
$$c$$
:

$$$10^c=1,000$$$

Factor 10 from 1,000:

$$$\frac{1,000}{10}=100\rightarrow \frac{100}{10}=10$$$

$$10$$
even appears three times in
$$1,000$$
. Thus,

$$$log_{10}(10^3)=3$$$

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