Question
Solve the following equations for x: $4^{\text{x}-1}\times(0.5)^{3-2\text{x}}=\Big(\frac{1}{8}\Big)^\text{x}$
✓
Answer
We have,$4^{\text{x}-1}\times(0.5)^{3-2\text{x}}=\Big(\frac{1}{8}\Big)^\text{x}$
$2^{2\text{x}-2}\times\Big(\frac{1}{2}\Big)^{3-2\text{x}}=\Big(\frac{1}{2}\Big)^{3\text{x}}$
$2^{2\text{x}-2}\times2^{2\text{x}-3}=\Big(\frac{1}{2}\Big)^{3\text{x}}$
$2^{2\text{x}-2+2\text{x}-3}=\Big(\frac{1}{2}\Big)^{3\text{x}}$
$2^{4\text{x}-5}=2^{-3\text{x}}$
$4\text{x}-5=-3\text{x}$
$7\text{x}=5$
$\text{x}=\frac{5}{7}$
$2^{2\text{x}-2}\times\Big(\frac{1}{2}\Big)^{3-2\text{x}}=\Big(\frac{1}{2}\Big)^{3\text{x}}$
$2^{2\text{x}-2}\times2^{2\text{x}-3}=\Big(\frac{1}{2}\Big)^{3\text{x}}$
$2^{2\text{x}-2+2\text{x}-3}=\Big(\frac{1}{2}\Big)^{3\text{x}}$
$2^{4\text{x}-5}=2^{-3\text{x}}$
$4\text{x}-5=-3\text{x}$
$7\text{x}=5$
$\text{x}=\frac{5}{7}$
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