Question

Find the value of x:
${(15\times 0.40)}^4÷{(1080÷30)}^4\times {(27\times 8)}^4={(3\times 2)}^{x+5}$

• A. 3
• B. 4
• C. 5
• D. None of these

Answer 1

The correct option is C

5

${(15\times 0.40)}^4÷{(1080÷30)}^4\times {(27\times 8)}^4={(3\times 2)}^{x+5}$
Or, $(6{)}^4\times (36{)}^4\times (27\times 8{)}^4={3\times 2}^{x+5}$
Or, $(6{)}^4÷{\left(\frac{1}{6}\right)}^8\times (27\times 8{)}^4=(3\times 2{)}^{x+5}$
Or, ${\left(\frac{1}{6}\right)}^4\times (3\times 3\times 3\times 2\times 2\times 2{)}^4=(3\times 2{)}^{x+5}$
Or, ${\left(\frac{1}{6}\right)}^4\times (6{)}^4\times (3\times 3\times 2\times 2{)}^4=(3\times 2{)}^{x+5}$
Or, $(3\times 2{)}^8=(3\times 2{)}^{x+5}$
Or, 8 = x + 5
Or, x = 3