Question

Please solve Q. 13 as in pic

Answer 1

Hi friend
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Your answer
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First

$7 {}^{x} + 5 {}^{y} = 74 \\ \\ = > 7 {}^{x} + 5 {}^{y} = 49 + 25 \\ \\ = > 7 {}^{x} + 5 {}^{y} = (7) {}^{2} + (5) {}^{2} \\ \\ so \\ \\ x = 2 \: and \: y = 2$
Second

$7 {}^{x + 1} - 5 {}^{y + 1} = 218 \\ \\ = > 7 {}^{x + 1} - 5 {}^{y + 1} = 343 - 125 \\ \\ = > 7 {}^{x + 1} - 5 {}^{y + 1} = (7) {}^{2 + 1} - 5 {}^{2 + 1} \\ \\ = > 7 {}^{x + 1} - 5 {}^{y + 1} = (7) {}^{3} - 5 {}^{3} \\ \\ so \\ \\ x + 1 = 3 \: and \: y + 1 = 3 \\ \\ x = 2 \: and \: y = 2$
HOPE IT HELPS