Question

$if \: {5}^{x} {} ^ + {} {}^{3} \times 3 {}^{2} {}^{x} {}^ - {} {}^{8} = 225 \: find \: x$
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Answer 1

Answer:

${5}^{x - 3} \times {3}^{2x - 8} = 225 \\ we \: can \: write \: 225 \: as \: 3 \times 3 \times 5 \times 5 \\ 225 = 3 \times 3 \times 5 \times 5 \\ therefore \: {5}^{x - 3} \times {3}^{2x - 8} = {5}^{2} \times {3}^{2} \\ on \: compairing \: we \: get \\ {5}^{x - 3} = {5}^{2} \: \: and \: \: {3}^{2x - 8} = {3}^{2} \\ x - 3 = 2 \: \: and \: \: 2x - 8 = 2 \\ x = 2 + 3 \: \: and \: \: 2x = 2 + 8 \\ x = 5 \: \: and \: \: x = \frac{10}{2} = 5 \\ so \: the \: value \: of \: x \: is \: 5$

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