Question

4 to the power x-1 × (0.5)to the power3-2x = (1/8)to the power x

Answer 1

I think we have to find x
${4}^{x - 1} \times {0.5}^{3 - 2x} = {1 \div 8}^{x}$
${ {2}^{2} }^{x - 1} \times { \frac{1}{2} }^{3 - 2x} = { \frac{1}{ {2}^{3} } }^{x}$
${2}^{2x - 2} \times { {2}^{ - 1} }^{ 3 - 2x} = { {2}^{ - 3} }^{x}$
${2}^{2x - 2} \times {2}^{ - 3 + 2x} = {2}^{ - 3x}$
${2}^{2x - 2 + ( - 3 + 2x)} = {2}^{ - 3x}$
thus by comp. LHS and RHS we got that
$2x - 2 - 3 + 2x = - 3x \\ \\ 4x - 5 = - 3x \\ \\ 7x = 5 \\ x = \frac{5}{7}$
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