Question

If 9x – 9x – 1 = 648, then find the value of xx

Answer 1

Correct question :-

If 9^x - 9^{x - 1} = 648, then find the value of x^x.

Answer :-

The value of x^x is 27.

Solution :-

$\sf 9^x - 9^{x - 1} = 648 \\\\\\ \sf \implies 9^x - 9^{x + ( - 1)} = 648 \\\\\\ \sf \implies 9^x - 9^x(9^{ - 1} ) = 648 \\\\\\ \bf \because {a}^{m +n} = {a}^{m} \times {a}^{n} \\\\\\ \sf \implies 9^x(1 - 9^{ - 1}) = 648 \\\\\\ \sf \implies 9^x \bigg(1 - \dfrac{1}{9^1} \bigg) = 648 \\\\\\ \bf \because {a}^{ - n} = \dfrac{1}{ {a}^{n} } \\\\\\ \sf \implies 9^x \bigg(1 - \dfrac{1}{9} \bigg) = 648 \\\\\\ \sf \implies 9^x \bigg( \dfrac{9 - 1}{9} \bigg) = 648\\\\\\ \sf \implies 9^x \bigg( \dfrac{8}{9} \bigg) = 648\\\\\\ \sf \implies 9^x = \dfrac{648 \times 9}{8} \\\\\\ \sf \implies 9^x = 81 \times 9 \\\\\\ \sf \implies 9^x =9^3 \\\\ \\ \sf \implies x = 3 \\\\\\ \bf \because if \: \: {a}^{m} = {a}^{n}\: \: then \: \: m = n$

Now find the value of x^x by bubstituting x = 3

x^x = 3³ = 27

Therefore the value of x^x is 27.