Question

write the value of n in each of the following
plz solve this problem ​

Answer 1

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★Solution:-

$\frac{5 {}^{n} \times 5 {}^{3} \times 5 {}^{ - 2} }{ {5}^{ - 5} } = {5}^{12} \\ \\ \\ \implies\frac{5 {}^{n + 3 - 2} }{ {5}^ { - 5} } = {5}^{12} \\ \\ \\ \implies \frac{5 {}^{n + 1} }{ {5}^{ - 5} } = {5}^{12} \\ \\ \\ \implies \: {5}^{n + 1 - ( - 5)} = {5}^{12} \\ \ \\ \ \implies \: {5}^{n + 1 + 5} = {5}^{12} \\ \\ \\ \implies {5}^{n + 6} = {5}^{12} \\ \\ \\ \implies \: n + 6 = 12 \\ \\ \\ \implies \: n = 12 - 6 \\ \ \\ \ \\ \implies \boxed { n = 6}$

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Done! :D

Answer 2

1) $\huge \tt{\frac{{\color{blue}{5}^{n} \times {5}^{3} \times {5}^{ - 2}}} {\color{blue}{ {5}^{ - 5} }}} = {\color{lightgreen}{5}^{12}}$

$\huge \Rightarrow \frac{\tt{\color{blue} {5}^{n + 3 + ( - 2)} }}{\color{blue}{ {5}^{ - 5}}} = {\tt{\color{lightgreen}{5}^{12}}}$

$\huge \Rightarrow \frac{\tt{\color{blue} {5}^{n + 1} }}{ \tt{\color{blue} {5}^{ - 5} }} = \tt{ \color{lightgreen} {5}^{12} }$

$\large\Rightarrow\tt{\color{blue} {5}^{n + 1 - ( - 5)}} = \tt{\color{lightgreen} {5}^{12} }$

$\huge\Rightarrow \tt{\color{blue} {5}^{n + 1 + 5 } } = \tt{\color{lightgreen} {5}^{12} }$

$\huge\Rightarrow \tt{\color{blue} {5}^{n + 6} } = \tt{\color{lightgreen} {5}^{12} }$

As we know that if exponents have same base so their exponents will also be same!!!

so,

$\: \ \: \: \: \: \: \: \: \Rightarrow \large\tt{\color{blue}n + 6} = \tt{\color{lightgreen}12}$

$\large \: \: \: \: \: \: \: \: \: \: \: \Rightarrow\tt{\color{blue}n} = \tt{\color{lightgreen}12 - 6}$

$\large \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \Rightarrow\boxed{\tt{\color{blue}n} = \tt{\color{lightgreen}6}}$

So n = 6