Base 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
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