Question

${5}^{x - 2 } \times {3}^{2x - 3} = 135$
Find the value of x. Chapter- exponents ​

Answer 1

Answer:

X= 3

Step-by-step explanation:

Given equation

${5}^{x - 2} \times {3}^{2x - 3} = 135$

Solution here

$135 = {5}^{x - 2} \times {3}^{2x - 3} \\ \\ 3 \times 45 = {5}^{x - 2} \times {3}^{2x - 3} \\ \\ 3 \times 3 \times 15 = {5}^{x - 2} \times {3}^{2x - 3} \\ \\ 3 \times 3 \times 3 \times 5 = {5}^{x - 2} \times {3}^{2x - 3} \\ \\ {3}^{3} \times {5}^{1} = {5}^{x - 2} \times {3}^{2x - 3} \\ \\ \therefore \: x - 2 = </strong><strong>1</strong><strong> \\ \\ \therefore \: x = </strong><strong>1</strong><strong>+ 2 = </strong><strong>3</strong><strong>....ans(1) \\ \\ 2x - 3 = </strong><strong>3</strong><strong>\\ \\ \therefore \: 2x = </strong><strong>3</strong><strong> + 3 \\ \\ \therefore \: 2x = </strong><strong>6</strong><strong>\\ \\ \therefore \: x = </strong><strong>3</strong><strong>...ans(2)$