Question

How do you solve $ 6{e^{5x - 6}} - 4 = 50 $ ?

Answer 1

Hint: In this question, we are provided with exponential expression. The first step would be taken to take all the constants to one side then by taking the logarithm we will eliminate the exponential term. Then simply find the value of $ x $

Complete step by step solution:
In the question, we are given an expression and from that we have to find the value of $ x $
 $ 6{e^{5x - 6}} - 4 = 50 $
Firstly, taking all the constants at one side. Just keep in mind, on changing the side signs will change from positive to negative sign and vice-versa.
  $ 6{e^{5x - 6}} = 50 + 4 = 54 $
Now, dividing both sides by $ 6 $ so that all the constants would come to one side.
 $ {e^{5x - 6}} = \dfrac{{54}}{6} = 9 $
Now, taking logarithm both sides
 $ 5x - 6 = \log (9) $
Finding value of $ x $ by simple calculations.
 $
\Rightarrow 5x = \log 9 + 6 \\
\Rightarrow x = \dfrac{{\log (9) + 6}}{5} \;
 $
We can also write
 $ \log 9 = \log {\left( 3 \right)^2} = 2\log 3 $
So, the required answer would be
 $ \Rightarrow x = \dfrac{{2\log 3 + 6}}{5} $
Putting $ log3 = 0.477 $
Hence, the answer is $ x = 1.63 $
So, the correct answer is “ $ x = 1.63 $ ”.

Note: When we are given such expressions to solve, choose your step wisely. Keep in mind to take all the constants to one side first. Then take the next step according to our convenience. Every student has their way of making the solution easier. So, you can take our own steps to solve the question.