Answer
398.1k+ views
Hint: By using the transformations, we can make the given question very easy to do. From the question given we have been asked to solve \[243={{9}^{2X+1}}\]. We know that we can express 243 as well as 9 as a power of 3. Then, we will make use of formula \[\Rightarrow {{\left( {{a}^{x}} \right)}^{y}}={{a}^{xy}}\] and simplify further to get the value of x.
Complete step-by-step solution:
From the question it had been given that \[243={{9}^{2X+1}}\]
\[\Rightarrow 243={{9}^{2X+1}}\]
We know that \[243\] can be written as \[{{3}^{5}}\]
By substituting it in the given question, we get the below equation,
\[\Rightarrow {{3}^{5}}={{9}^{2X+1}}\]
Similarly, we know that \[9\] can be written as \[{{3}^{2}}\]
Now, we know the basic formula of exponents,
\[\Rightarrow {{\left( {{a}^{x}} \right)}^{y}}={{a}^{xy}}\]
By substituting it in the given question, we get the below equation, and
By using the above basic formula of exponents, we get,
\[\Rightarrow {{3}^{5}}={{3}^{2\left( 2x+1 \right)}}\]
As the bases are equal in the above equation, we can equate the indices or powers.
By equating the indices or powers of the above equation, we get,
\[\Rightarrow 5=2\left( 2x+1 \right)\]
Furthermore simplifying the above equation we get,
\[\Rightarrow 5=4x+2\]
Now, take of\[2\] from both sides we get,
\[\Rightarrow 5-2=4x+2-2\]
\[\Rightarrow 3=4x\]
Now, divide both sides with \[4\] we get,
\[\Rightarrow x=\dfrac{3}{4}\]
Hence, the given equation is simplified.
Note: Students should be well aware of the exponents and powers. Students should be very careful while doing the calculation we should not make mistakes like here in this question \[\Rightarrow 243={{9}^{2x+1}}\] we should not equate \[\Rightarrow 5=2x+1\] like this we should equate it to \[\Rightarrow 5=4x+2\] to get answer in this type of problems as calculation part is somewhat difficult in this type of problems. Students should know which type of transformation is to be used for the given question to get the question into an easier way.
Complete step-by-step solution:
From the question it had been given that \[243={{9}^{2X+1}}\]
\[\Rightarrow 243={{9}^{2X+1}}\]
We know that \[243\] can be written as \[{{3}^{5}}\]
By substituting it in the given question, we get the below equation,
\[\Rightarrow {{3}^{5}}={{9}^{2X+1}}\]
Similarly, we know that \[9\] can be written as \[{{3}^{2}}\]
Now, we know the basic formula of exponents,
\[\Rightarrow {{\left( {{a}^{x}} \right)}^{y}}={{a}^{xy}}\]
By substituting it in the given question, we get the below equation, and
By using the above basic formula of exponents, we get,
\[\Rightarrow {{3}^{5}}={{3}^{2\left( 2x+1 \right)}}\]
As the bases are equal in the above equation, we can equate the indices or powers.
By equating the indices or powers of the above equation, we get,
\[\Rightarrow 5=2\left( 2x+1 \right)\]
Furthermore simplifying the above equation we get,
\[\Rightarrow 5=4x+2\]
Now, take of\[2\] from both sides we get,
\[\Rightarrow 5-2=4x+2-2\]
\[\Rightarrow 3=4x\]
Now, divide both sides with \[4\] we get,
\[\Rightarrow x=\dfrac{3}{4}\]
Hence, the given equation is simplified.
Note: Students should be well aware of the exponents and powers. Students should be very careful while doing the calculation we should not make mistakes like here in this question \[\Rightarrow 243={{9}^{2x+1}}\] we should not equate \[\Rightarrow 5=2x+1\] like this we should equate it to \[\Rightarrow 5=4x+2\] to get answer in this type of problems as calculation part is somewhat difficult in this type of problems. Students should know which type of transformation is to be used for the given question to get the question into an easier way.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science 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)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 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)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![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)
How do you graph the function fx 4x class 9 maths 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)