Question

25 ki power x is equal to 25 upon 5 ki power x

Answer 1

Heya dear user !!!

Here is your answer,

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${(25)}^{x} = \frac{25}{ {(5)}^{x} } \\ \\ {( {5}^{2} )}^{x} = \frac{ ({5)}^{2} }{ {(5)}^{x} } \\ \\ {(5)}^{2x} = {(5)}^{2 - x} \\ \\ bases \: \: are \: \: same \: \\ now \: \: equating \: \: their \: \: powers \\ \\ 2x = 2 - x \\ \\ 2x + x = 2 \\ \\ 3x = 2 \\ \\ x = \frac{2}{3}$

Verification
$L.H.S = {(25)}^{x } \\ \\ = {(25)}^{ \frac{2}{3} } \\ \\ = {(5)}^{2 \times \frac{2}{3} } \\ \\ = {(5)}^{ \frac{4}{3} } \\ \\ \\ R.H.S = \frac{ 25 }{ {(5)}^{x} } \\ \\ = \frac{ {(5)}^{2} }{ {(5)}^{ \frac{2}{3} } } \\ \\ = ({5)}^{2 - \frac{2}{3} } \\ \\ = {(5)}^{ \frac{6 - 2}{3} } \\ \\ = {(5)}^{ \frac{4}{3} }$

Hence, L.H.S = R.H.S (verified)

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Hope it helps.

Answer 2

$hey \: here \:is \: your \: answer \\ \\ 25 ^{x} = 25 \div 5 ^{x} \\ 5 ^{2} x \: = 5 ^{2} \ \div 5 ^{x} \\ 5 ^{2} x = 5 ^(2 \ - x) \\ \\ 2x = 2 - x \\ 2x + x = 2 \\ 3x = 2 \\ x = 2 \div 3$


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