
The value of x, which satisfies is
A.
B.
C.
D.
Answer
489.9k+ views
Hint: In this question use the concept of logarithm and also remember the relation between common logarithm and natural logarithm i.e. log and ln which is given as; or and use the formula to approach the solution.
Complete step-by-step answer:
According to the given information we have equation
We have to find the value of x so now (equation 1)
Now let’s divide equation (1) by both the sides, we have
We can write the above equation as
(equation 2)
Let us substitute in equation 2
If we have a quadratic equation of the form
Then the roots of equation of this form is written as .
Now using the above to solve for the roots of equation
So, we get 2 values of y that is ,
Now we have substituted , so let’s substitute it back
So
But is not possible since will always be positive irrespective of value of x as exponential values aren’t negative.
So only value left with us is
Now take log both sides, so we get
So, on simplifying
Now using the property of logarithm that
We have
As we know that or
Therefore,
After simplifying the above equation, we get
Therefore, the value of x is equal to
So, the correct answer is “Option C”.
Note: Whenever we face such types of problems the key step that we need we have in our mind is that we always try and form a quadratic equation by proper simplification and substitution. This quadratic equation thus formed can be easily solved (roots can be calculated) using the formula of quadratic formula for quadratic equations mentioned above.
Complete step-by-step answer:
According to the given information we have equation
We have to find the value of x so now
Now let’s divide equation (1) by
We can write the above equation as
Let us substitute
If we have a quadratic equation of the form
Then the roots of equation of this form is written as
Now using the above to solve for the roots of equation
So, we get 2 values of y that is
Now we have substituted
So
But
So only value left with us is
Now take log both sides, so we get
So, on simplifying
Now using the property of logarithm that
We have
As we know that
Therefore,
After simplifying the above equation, we get
Therefore, the value of x is equal to
So, the correct answer is “Option C”.
Note: Whenever we face such types of problems the key step that we need we have in our mind is that we always try and form a quadratic equation by proper simplification and substitution. This quadratic equation thus formed can be easily solved (roots can be calculated) using the formula of quadratic formula for quadratic equations mentioned above.
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