Question

How do you solve \[\log x = 3\]?

Answer 1

Hint:In the given question, we have been given an expression. This expression contains a function. The function has a constant as its argument. This constant is a variable. The whole function is equal to a natural number. We have to solve for the value of this expression. This can be easily done if we know the property of the function with exponents.
Formula Used:
We are going to use the formula of logarithm, which is:
\[{\log _b}a = n \Rightarrow {b^n} = a\]

Complete step by step answer:
The given expression is \[\log x = 3\].
The basic formula of logarithm says,
If \[{\log _b}a = n\]
then, \[{b^n} = a\]
In the question, we have not been given the value of \[b\] (base). This is a standard representation. It is the same as the value of the base that we use in the normal day numbers – \[10\].
Hence, putting \[b = 10\], \[a = x\] and \[n = 3\], we get,
\[{\log _{10}}x = 3\]

Hence, \[x = {10^3} = 100\]

Additional Information:
The \[\log \] function has other basic properties too:
\[{\log _x}{x^n} = n\]
\[{\log _a}b = \dfrac{1}{{{{\log }_b}a}}\]

Note: In this question, to solve for the answer, we needed to know the properties of the logarithmic function. We need to know the base of the number when nothing is given. We follow the standard base as used in the normal numbers – the base of Ten. So, all we needed to do is raise ten to the power of three and we got the answer, the value of the variable – thousand.