Question

Solve $ 2{e^x} - 5 = 1 $ ?

Answer 1

Hint: Given an expression of the form $ {e^x} $. To solve the expression containing $ {e^x} $ first we'll put like terms on one side. For example terms of coefficient of $ {e^x} $ on one side and numerical on one side. After doing addition or subtraction of digits then we will do the division of numbers formed by the coefficient of $ {e^x} $. To find the value of x will take log with base e on both sides then we will apply the property that
 $ {\log _e}e = 1 $
 Log with the same base and same number is equal to 1. By applying this will get the value of x in form of log then using the log table we can find the value of log and put it into it.

Complete step by step answer:
Step1:
We are given an expression $ 2{e^x} - 5 = 1 $ now first we will arrange like terms on two different sides
 $ \Rightarrow 2{e^x} = 1 + 5 $
Adding like terms we get:
 $ \Rightarrow 2{e^x} = 6 $
Now we will divide the 6 by the coefficient of $ {e^x} $ i.e. 2
 $ \Rightarrow {e^x} = \dfrac{6}{2} $
 $ \Rightarrow {e^x} = 3 $

Step2:
To find the value of x we will take lo9g on both sides
 $ \Rightarrow {\log _e}{e^x} = {\log _e}3 $
First we will use the property $ \log {m^n} = n\log m $
 $ \Rightarrow x{\log _e}e = {\log _e}3 $
Using the property $ {\log _e}e = 1 $ we will get:
 $ \Rightarrow x = {\log _e}3 $

Step3:
Now using the log table we will find the value of $ {\log _e}3 $ and substitute in the expression.
 $ \Rightarrow x = 0.4771 $

Note: In such types of questions having $ {e^x} $. Students did not get an approach how to solve. But to solve the questions of exponents take the log both sides of the equation. By using the property first we will use the property $ \log {m^n} = n\log m $. Then $ {\log _e}e = 1 $. Similarly for $ {10^x} $ we will take log both sides here log will be of base 10. So by using this property we can solve these types of questions of exponents.