Question

solve question 1 . and d ​

Answer 1

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Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: QUESTION \: \: } \mid}}}}}$

$\: \: \: \: \: \texttt{Find the value of \red{n} : } \\ \\ \: \: \: \: \: \: \: \: \: \: \tt{9 {}^{n + 1} - 9 {}^{n} = 72}$

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\: \: \: \: \: \: \: \: \: \: \tt{9 {}^{n + 1} - 9 {}^{n} = 72} \\ \\ \tt{ \implies \: 9 {}^{n}.9 {}^{1} - 9 {}^{n} = 72} \\ \\\tt{ \implies \: 9 {}^{n}.9 - 9 {}^{n}.1 = 72 }\\ \\ \tt{ \implies \: 9 {}^{ {}^{n} } . (9 - 1) = 72} \\ \\ \tt{ \implies \: 9 {}^{n}.8 = 72} \\ \\ \tt{ \implies \: 9 {}^{n} = \frac{72}{8}} \\ \\\tt{ \implies \: 9 {}^{n} = 9} \\ \\ \tt{ \implies \: 9 {}^{n} = 9 {}^{1}} \\ \\ \: \: \: \: \: \: \: \: \: \bf{ \therefore\: \red{ \underline{ \: n = 1 \: }}}$

$\underline{ \underline{ \sf{ \large{ \: \star \: \: \: IDENTITIES \: \: USED \: \: \: \star \: }}}}$

$\bf{ 1. \: \: \pink{a {}^{m + n} = a {}^{m} + a {}^{n}}} \\ \\ \bf{2. \: \: \pink{a = a {}^{1}}} \\ \\ \bf{ 3. \: If \: \: \pink{ a {}^{m} = a {}^{n}} ,then \: \: \pink{m = n}}$