Question

find the value of x if -
${5 }^{2x + 1} \div 25 = 125$
​

Answer 1

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\sf \bf {5}^{2x + 1} \div 25 = 125$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf\implies {5}^{2x + 1} \div 25 = 125$

$\sf \bf\implies {5}^{2x + 1} \div {5}^{2} = {5}^{3}$

$\sf \bf\implies {5}^{2x + 1-2}= {5}^{3}$

$\tt {\underbrace {Now\: equate\: only\: the\: powers}}$

$\sf \bf \implies 2x+1-2=3$

$\sf \bf \implies 2x-1=3$

$\sf \bf \implies 2x=3+1$

$\sf \bf \implies 2x=4$

$\sf \bf \implies x=\dfrac{4}{2}$

$\implies{\boxed {\color {green} {\sf \bf x=2}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

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$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\tt \underline{Identities}$

$\sf \bf {(a+b)}^{2}={a}^{2}+2ab+{b}^{2}$

$\sf \bf {(a-b)}^{2}={a}^{2}-2ab+{b}^{2}$

$\sf \bf (a+b) (a-b) ={a}^{2}-{b}^{2}$

${\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {lime} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {aqua} {@suraj5070}}}}}}}}}}}}}}}$