Question

If \[\log x = 0\], then the value of \[x = ?\]

Answer 1

Hint: In this question, first of all identify the base of the given logarithm and use the formula to convert the given logarithm in terms of base and power to get the required solution.

Complete step-by-step answer:
Given that \[\log x = 0\]
We know that a natural logarithm has a base value of \[e = 2.718\].
So, we have \[{\log _e}x = 0\]
We know that, if \[{\log _a}b = c\] then \[{a^c} = b\].
By using this statement, we have
\[
   \Rightarrow {\log _e}x = 0 \\
   \Rightarrow {e^0} = x \\
   \Rightarrow 1 = x{\text{ }}\left[ {\because {e^0} = 1} \right] \\
  \therefore x = 1 \\
\]
Thus, the value of \[x\] is 1 i.e., \[x = 1\].

Note: A natural logarithm has a base value of \[e = 2.718\]. Always remember that anything power zero is equal to one. If \[{\log _a}b = c\] then \[{a^c} = b\] and vice versa.