Question

if (5)^x-3.(3)^2x-8 = 225. find x

Answer 1

${5}^{x - 3} \times {3}^{2x - 8} = 225 \\ \\ {5}^{x - 3} \times {3}^{2x - 8} = {5}^{2} \times {3 }^{2} \\ \\ {5}^{x - 3} = {5}^{2} \\ \\ {3}^{2x - 8} = {3}^{2} \\ \\ \bf \: If \: the \: numbers \: are \: equal \: then \\ \: \bf \: we \: can \: put \: powers \: equal \: : \\ \\ x - 3 = 2 \: \: \: \: \: \: \: \: ...(i) \\ \\ 2x - 8 = 2 \: \: \: \: \: \: \: \: ...(ii) \\ \\ \bf \: Solving \: both \: the \: equations \\ \bf \: we \: get : \\ \\ x = 5 \\ \\ 2x = 10 \\ \\ x = 5 \\ \\ \bf \: So \: the \: value \: of \: x \: is \: 5.$

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