Question

If
${5}^{x - 2} \times {3}^{2x - 3} = 135$
find the value of x
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Answer 1

Answer:

Hey Hi

$= {5}^{x - 2} \times {3}^{2x - 3} = 135 \\ \\ = {5}^{x - 2} \times {3}^{2x - 3} =27 \times 5 \\ \\ = {5}^{x - 2} \times {3}^{2x - 3} = {3}^{3} \times {5}^{1} \\ \\ = {5}^{x - 2 - 1} \times {3}^{2x - 3 - 3} = 1 \\ \\ = {5}^{x - 3} \times {3}^{2x - 6} = 1 \\ \\ = {5}^{x - 3} \times {3}^{2(x - 3)} = 1 \\ \\ = {5}^{x - 3} \times {9}^{x - 3} = 1 \\ \\ {5 \times 9}^{x - 3} = {1}^{x - 3} \\ \\ {45}^{x - 3} = 1$

Now we know any number to the power 0 is 1

Thus

$x - 3 = 0 \\ \\ x = 3$

Hope this helps

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Rishabh Bansal

Answer 2

${5}^{x - 2} \times {3}^{2x - 3} = 135 \\ => {5}^{x - 2} \times {2}^{2x - 3} = 5 \times {3}^{3} \\ => x - 2 = 1 \: and \: 2x - 3 = 3 \\ => x = 3$