Question
Question: How do you solve \( \ln x = - 7? \)...
How do you solve lnx=−7?
Solution
Let us understand in a general way, the function of a logarithm, Consider a logarithm of a with base b equal to c , it means that when c is raised to the power of b then it will equal to a , let’s understand this in mathematical way or in equations ⇒logba=c It is the mathematical form of the first part of the consideration. Now coming to the second part ⇒bc=a It is the mathematical form of the second part. Hope that you got to understand the logarithmic function. ln is a special logarithmic function which has a fixed base equals e Try to write the problem in equation form and then solve it further.
Complete step by step solution:
We have to find the value of x using some properties logarithm and
exponential, Now let’s come to the question, we have lnx=−7 , we can also write this in log form as
logex=−7 _____(I)
Logarithmic function has a property that if it is raised on the power of its base then only argument of the logarithm left, let us understand this with an example logab , if we raise logab in the power of a then only b will left
⇒alogab=b
Now we will raise both sides of equation (I) on the power of e , we will get
⇒elogex=e−7 ⇒x=e−7
We got the required solution for lnx=−7 which is x=e−7
If you want numerical value then calculate this on a calculator you will get a value close to x=9.12×10−4
Note: The functions y=ex&y=lnx are inverse functions of each other. Base of a logarithm function should be greater than zero and can’t be equal to one.
Argument of the logarithm function is always positive.