Question

Find the value of p if [5^ (p-3) ] * [3^ (2p-8) ] = 225

I WILL MARK AS BRAINLIEST TO THE PERON WHO ANSWERS IT CORRECTLY.

Answer 1

Answer:

${5}^{ p- 3} \times {3}^{2p - 8} = 225$

${5}^{p - 3} \times {3}^{2p - 8} = {3}^{2} \times {5}^{2}$

$\frac{ {5}^{ p- 3} }{ {5}^{2} } \times \frac{ {3}^{2p - 8} }{ {3}^{2} } = 1$

${5}^{ p- 3 - 2} \times {3}^{2p - 8 - 2} = 1$

${5}^{ p- 5} \times {3}^{2p - 10} = 1$

${5}^{p - 5} \times( {3}^{2}) {}^{p - 5} = 1$

$(5 \times 9) {}^{p - 5} = 1$

${45}^{p - 5} = {45}^{0}$

$p - 5 = 0$

$p = 5$

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