Question

Find the value of x if
${3}^{2x - 1} \div 9 = 27$
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Answer 1

Question:

Find the value of x if ${3}^{2x-1} \div 9 = 27$

Answer:

${3}^{2x - 1} \div 9 = 27$

${3}^{2x - 1} \div {3}^{2} = {3}^{3}$

${3}^{2x - 1 - 2} = {3}^{3}$

${3}^{2x - 3} = {3}^{3}$

On equating the powers of 3,

2x-3 = 3

2x = 3+3

2x = 6

$x = \frac{6}{2}$

x = 3

☆ The value of x is 3.

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⭐CONCEPTS USED⭐

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$a^{m} \div a^{n} = a^{m-n}$

Check:

By putting the value of x as 3 in the equation,

${3}^{2×3-1} \div 9 = 27$

${3}^{6-1} \div 9 = 27$

${3}^{5} \div 9 = 27$

${3}^{5} \div {3}^{2} = {3}^{3}$

${3}^{5-2} = {3}^{3}$

${3}^{3} = {3}^{3}$

27 = 27,

LHS = RHS

Hence Verified