Question

How do you solve $\log \,x\, = \, - 2$?

Answer 1

Hint:
A logarithm is the power to which a number must be raised in order to get some other number. For example, the logarithm with base 10 of 1000 is 3, because ten raised to the power of three is 1000. The base unit is the number to which the power is raised.

Complete step by step solution:
There are logarithms with different base units.
In this case the base logarithm of $x$ is $ - 2$, because ten raised to the power of minus two is x:
$\log x = - 2$
Because
\[x\, = \,{10^{ - 2}}\]
Using exponents, the negative power represents that it can be written as the inverse of the number.
$ = \,\left( {\dfrac{1}{{{{10}^2}}}} \right)$
${10^2}$ means multiplication of 10 two times or square of ten.
Then, we can write
$ = \,\dfrac{1}{{100}}$
Which is nothing but equals to
$ = \,0.01$
So, by solving $\log \,x\, = \, - 2$ , we will get the value of x as $\,0.01$ .
Where, $\,0.01$ is a positive integer.

the correct answer is $\,0.01$.

Additional information:
In general, we write log which is then followed by the base number. The most common logarithms are base 10 logarithms and natural logarithms. A base ten log is written as
$\log $
and a base ten logarithmic equation is written in the form of :
$\log x\, = \,a$
In logarithm if the base is 3, then it can be written as ${\log _3}x\, = \,a$.
The natural log is written as $\ln \,x$. So, when you see log by itself, it means base ten log.

Note:
The exponent of a number says how many times to use the number in a multiplication and the number of times it gets multiplied becomes its power.