Question

How do you solve $ \log (4x - 1) = 5 $ ?

Answer 1

Hint:According to the given question, we have to solve $ \log (4x - 1) = 5 $ .
So, first of all we have to convert the R.H.S. term of the given question into the logarithmic term.
So, we have to remember that the given digit in the question as $ 5 $ is equal to $ 5 \times 1 $ .
Now, we have to remember that $ \log 10 = 1 $ and convert the just above sentence into the logarithmic function by putting $ 1 = \log 10 $ .
Now, we have to compare both L.H.S and R.H.S terms and find the value of $ x. $

Complete step by step answer:
Step 1: first of all we have to convert the R.H.S. term of the given question into the logarithmic term, as we know that the given digit in the question as $ 5 $ is equal to $ 5 \times 1 $ and $ 1 = \log 10 $ .
 $ \Rightarrow $ $ \log (4x - 1) = 5 \times 1 $
 $ \Rightarrow \log (4x - 1) = 5 \times \log 10 $
Step 2: First of all we know that $ m\log n = \log {n^m} $ , so apply this concept into the expression obtain in the solution step1.
 $ \Rightarrow \log (4x - 1) = \log {10^5} $
Step 3: Now, we have to compare both L.H.S and R.H.S term of the expression obtain in the solution step 2.
  $ \Rightarrow (4x - 1) = {10^5} $
Now, we have to solve the above expression and find the value of $ x. $
 $
   \Rightarrow (4x - 1) = 100000 \\
   \Rightarrow 4x = 100000 + 1 \\
   \Rightarrow 4x = 100001 \\
   \Rightarrow x = \dfrac{{100001}}{4} \\
  $
Now, we have to divide the above number of nominators by 4 and get the value of $ x. $
 $ \Rightarrow x = 25000.25 $
Final solution: Hence, the solution of the given expression in the question as $ \log (4x - 1) = 5 $ is $ x = 25000.25 $ .

Note:
It is necessary to convert the R.H.S. term of the given question into the logarithmic term, so we have to compare both L.H.S and R.H.S term and find the value of $ x. $
It is necessary to remember that the given digit in the question as $ 5 $ is equal to $ 5 \times 1 $ .