Question

How do you calculate \[{{\log }_{10}}10000\].

Answer 1

Hint: In this problem, we have to calculate the value of \[{{\log }_{10}}10000\] by using simple logarithmic formulae. We know that \[{{\log }_{b}}x=y\]if \[{{b}^{y}}=x\]. Now we can assume the given equation as y and substitute the value of x and b to get the value of y, that is the solution, applying basic logarithmic formulae in that expression, we can find the value of the given problem. Here we have to know simple logarithmic formulae to do calculations to find the value of the given logarithmic expression.

Complete answer:
We are now given a logarithmic expression that is,
\[{{\log }_{10}}10000\]………. (1)
We know that the general form of base 10 logarithm,
\[{{\log }_{b}}x=y\]………. (2)
From (1) and (2), we can assume that,
\[\begin{align}
  & \Rightarrow y={{\log }_{10}}10000 \\
 & \Rightarrow y={{\log }_{10}}{{10}^{4}} \\
 & \because {{10}^{4}}=10000 \\
 & \Rightarrow y={{\log }_{10}}{{10}^{4}}........(3) \\
\end{align}\]
We know that, the base 10 logarithmic formula,
\[{{\log }_{10}}{{10}^{4}}=4{{\log }_{10}}10\]…….. (4)
Now we can apply the formula (4) in the expression (3), we get
\[\begin{align}
  & \Rightarrow y=4{{\log }_{10}}10 \\
 & \Rightarrow y=4\text{ }\because \text{lo}{{\text{g}}_{10}}10=1 \\
\end{align}\]
Therefore, the value of \[{{\log }_{10}}10000\] is 4.

Note:
Students should know that to solve these types of problems, we have to know basic logarithmic rules and formulae. Students should also know the log base 10 formula to solve these types of problems. Remember the formulae used in this sum \[{{\log }_{10}}{{10}^{4}}=4{{\log }_{10}}10\], \[\text{ lo}{{\text{g}}_{10}}10=1\] these are some of the formulae used in many problems based on logarithm. Students will make mistakes in writing the logarithmic formulas and should concentrate more in formulae part, to avoid minor mistakes.