If ${\log _{10}}\left( {x - 10} \right) = 1$, then the value of x is equal to:
  {\text{A}}{\text{. 20}} \\
  {\text{B}}{\text{. 30}} \\
  {\text{C}}{\text{. 40}} \\
  {\text{D}}{\text{. 50}} \\

Answer Verified Verified
Hint- In this question we have to find the value of x so using the property of logarithm we know that ${\log _b}a = 1 \Rightarrow {b^1} = a$. This property will help you simplify things up and will eventually help you reach the right answer.

We have been given the expression ${\log _{10}}\left( {x - 10} \right) = 1$ and we have to find the value of x.
Now we know the property of logarithm that ${\log _b}a = 1 \Rightarrow {b^1} = a$ ………………….. (1)
So using the property mentioned in equation (1) to the given expression of question we get
${10^1} = \left( {x - 10} \right)$
On solving
$10 = x - 10$
$ \Rightarrow x = 20$
Hence the value of x = 20
Thus option (a) is the right answer to this answer.

Note- Whenever we face such types of problems the key point to remember is that we need to have a good grasp over the logarithmic identities, some of them have been mentioned above. These identities help you in simplification and getting on the right track to reach the answer.
Bookmark added to your notes.
View Notes