Answer
384k+ views
Hint:For simplifying the original equation , take base ten exponential of both sides of the equation, then apply the logarithm formula ${b^{{{\log }_b}a}} = a$ to simplify the equation. Then recall that the logarithm function says $\log x$ is only defined when $x$ is greater than zero.
Formula used:
We used logarithm property i.e.
${b^{{{\log }_b}a}} = a$ , the logarithm function says $\log x$ is only defined when $x$ is greater than zero.
Complete solution step by step:
It is given that ,
$\log (2x - 1) = 3$
We have to solve for $x$ ,
Now , by assuming the base of the logarithm to be $10$ ,then take the base $10$ exponential of both sides of the equation, we will get the following result ,
${10^{{{\log }_{10}}(2x - 1)}} = {10^3}$
By applying the logarithm formula ${b^{{{\log }_b}a}} = a$ . we will get the following result ,
$2x - 1 = 1000$ ,
Now simplify the above equation as ,
$
\Rightarrow 2x = 1000 + 1 \\
\Rightarrow 2x = 1001 \\
\Rightarrow x = \dfrac{{1001}}{2} \\
$
Now recall that the logarithm function says $\log x$ is only defined when $x$ is greater than zero.
Therefore, in our original equation $\log (2x - 1) = 3$ ,
Here we must have ,
$(2x - 1) > 0$ ,
We have $x = \dfrac{{1001}}{2}$
We get ,
$1000 > 0$
Therefore, we have our solution i.e., $x = \dfrac{{1001}}{2}$ .
Note: The logarithm function says $\log x$ is only defined when $x$ is greater than zero. While defining logarithm function one should remember that the base of the log must be a positive real number and not equals to one . At the end we must recall that the logarithm function says $\log x$ is only defined when $x$ is greater than zero. While performing logarithm properties we have remember certain conditions , our end result must satisfy domain of that logarithm
Formula used:
We used logarithm property i.e.
${b^{{{\log }_b}a}} = a$ , the logarithm function says $\log x$ is only defined when $x$ is greater than zero.
Complete solution step by step:
It is given that ,
$\log (2x - 1) = 3$
We have to solve for $x$ ,
Now , by assuming the base of the logarithm to be $10$ ,then take the base $10$ exponential of both sides of the equation, we will get the following result ,
${10^{{{\log }_{10}}(2x - 1)}} = {10^3}$
By applying the logarithm formula ${b^{{{\log }_b}a}} = a$ . we will get the following result ,
$2x - 1 = 1000$ ,
Now simplify the above equation as ,
$
\Rightarrow 2x = 1000 + 1 \\
\Rightarrow 2x = 1001 \\
\Rightarrow x = \dfrac{{1001}}{2} \\
$
Now recall that the logarithm function says $\log x$ is only defined when $x$ is greater than zero.
Therefore, in our original equation $\log (2x - 1) = 3$ ,
Here we must have ,
$(2x - 1) > 0$ ,
We have $x = \dfrac{{1001}}{2}$
We get ,
$1000 > 0$
Therefore, we have our solution i.e., $x = \dfrac{{1001}}{2}$ .
Note: The logarithm function says $\log x$ is only defined when $x$ is greater than zero. While defining logarithm function one should remember that the base of the log must be a positive real number and not equals to one . At the end we must recall that the logarithm function says $\log x$ is only defined when $x$ is greater than zero. While performing logarithm properties we have remember certain conditions , our end result must satisfy domain of that logarithm
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)