Base Log
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
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,
$$$log_{10}(10^3)=3$$$
3
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