Question
Download Solution PDF\( \left( \frac{29}{4} \right)^3 \times \left( \frac{4}{29} \right)^2 \times \left( \frac{29}{4} \right)^{11} = \left( \frac{4}{29} \right)^{9m + 7}\) चे समाधान करेल असे m चे मूल्य शोधा.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिले आहे:
\(\displaystyle\Bigl(\frac{29}{4}\Bigr)^3\times\Bigl(\frac{4}{29}\Bigr)^2\times\Bigl(\frac{29}{4}\Bigr)^{11}=\Bigl(\frac{4}{29}\Bigr)^{9m+7}\)
वापरलेले सूत्र:
घातांकाचा नियम: \([\frac{a}{b}]^r=[\frac{b}{a}]^{-r}\)
ap × aq = ap + q
गणना:
\(\displaystyle\Bigl(\frac{29}{4}\Bigr)^3\times\Bigl(\frac{4}{29}\Bigr)^2\times\Bigl(\frac{29}{4}\Bigr)^{11}=\Bigl(\frac{4}{29}\Bigr)^{9m+7}\)
⇒ \(\displaystyle\Bigl(\frac{4}{29}\Bigr)^{-3}\times\Bigl(\frac{4}{29}\Bigr)^2\times\Bigl(\frac{4}{29}\Bigr)^{-11}=\Bigl(\frac{4}{29}\Bigr)^{9m+7}\)
⇒ \(\displaystyle\Bigl(\frac{4}{29}\Bigr)^{-3+ 2-11}=\Bigl(\frac{4}{29}\Bigr)^{9m+7}\)
⇒ \(\displaystyle\Bigl(\frac{4}{29}\Bigr)^{-12}=\Bigl(\frac{4}{29}\Bigr)^{9m+7}\)
⇒ -12 = 9m + 7
⇒ 12 + 7 = -9m
⇒ 19 = -9m
\(m = -\frac{19}{9}\)
∴ दिलेल्या समीकरणाचे समाधान करणारे m चे मूल्य \(-\frac{19}{9}\) आहे.
Last updated on Jul 19, 2025
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