Question

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 1

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.