Question

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Answer 1

Answer:

${5}^{x} + {5}^{x + 1} + {5}^{x + 2} = 775$

$775 = 31 \times {5}^{2}$

${5}^{x} + {5}^{x + 1} + {5}^{x + 2} = 31 \times {5}^{2}$

$considering \: \: {5}^{x} \: and \: {5}^{2} \: as \:they \:are \:on\\ \:either\: side\: of\: equation$

${5}^{x} = {5}^{2}$

$x = 2$

Now putting value of x in equation

${5}^{2} + {5}^{2 + 1} + {5}^{2 + 2} = 31 \times 25$

$25 + 125 + 625 = 775$

$775 = 775$

Hence, value of x is 2

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