mathematics-class-11-unit-10-chapter-10-sequence-and-series-l-10-10-0rm-pzn1-nm

### <Success>Problem 4</Success>
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<p>A piece of equipment cost a certain factory Rs. 600,000 . If it depreciates in value;<br>
$ 15 $ %the first year, $13.5 $ % the next year $12 $ % the third year and so on, what will be its value at the end of 10 years?</p>
<p>(All percentages applying to the Original cost)</p>
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<img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/mathematics-class-11-unit-10-chapter-10-sequence-and-series-l-10-10-0rm-pzn1-nM-20a.jpg">
<img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/mathematics-class-11-unit-10-chapter-10-sequence-and-series-l-10-10-0rm-pzn1-nM-20b.jpg"></p>

### <Success>Solution</Success>
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<p>$\log 2, \log \left(2^x-1\right)$ and $\log \left(2^x+3\right)$ are $\text { in } A \cdot P \text {. }$</p>
<p>$\therefore \log \left(2^x-1\right)=\frac{\log 2+\log \left(2^x+3\right)}{2}$</p>
<p>$ 2 \log \left(2^x-1\right) =\log 2+\log \left(2^x+3\right)$</p>
<p>$ =\log \left(2 \cdot\left(2^x+3\right)\right)$</p>
<p>$ \log \left(2^x-1\right)^2=\log \left(2 \cdot\left(2^x+3\right)\right)$</p>
<p>$ \left(2^x-1\right)^2=2 \cdot\left(2^x+3\right) $</p>
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<p><img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/mathematics-class-11-unit-10-chapter-10-sequence-and-series-l-10-10-0rm-pzn1-nM-34.jpg">
<img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/mathematics-class-11-unit-10-chapter-10-sequence-and-series-l-10-10-0rm-pzn1-nM-34a.jpg"></p>

### <Success>Solution</Success>
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<p>$ \left(2^x\right)^2-2 \cdot 2^x +1=2 \cdot 2^x+6$</p>
<p>$ \left(2^x\right)^2-4 \cdot 2^x-5=0$</p>
<p>Let $2^x=y$</p>
<p>$y^2-4 y-5=0 \text {. }$</p>
<p>Solving, $y=5$ or $y=-1$</p>
<p>i.e $2^x=5$ or $2^x=-1$</p>
<p>$ \therefore 2^x=5 $</p>
<p>$ {{x=\ln 2^5}} $</p>
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<img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/mathematics-class-11-unit-10-chapter-10-sequence-and-series-l-10-10-0rm-pzn1-nM-36a.jpg"></p>
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<p>======</p>
<h3 id="successthank-yousuccess"><Success>Thank you</Success></h3>
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