Solve the following equations: 4^ x-1 (0.5)^ 3-2x = (1 8 )^ x - Vidyadip

Question

Solve the following equations: $4^{\text{x}-1}\times(0.5)^{3-2\text{x}}=\Big(\frac{1}{8}\Big)^{\text{x}}$

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Answer

$4^{\text{x}-1}\times(0.5)^{3-2\text{x}}=\Big(\frac{1}{8}\Big)^{\text{x}}$$\Rightarrow(2^2)^{\text{x}-1}\times\Big(\frac{1}{2}\Big)^{3-2\text{x}}=\Big(\frac{1}{2^3}\Big)^\text{x}$
$\Rightarrow2^{2\text{x}-2}\times2^{-3+2\text{x}}=2^{-3\text{x}}$
$\Rightarrow2^{2\text{x}-2-3+2\text{x}}=2^{-3\text{x}}$
$\Rightarrow2^{4\text{x}-5}=2^{-3\text{x}}$
$\Rightarrow4\text{x}-5=-3\text{x}$
$\Rightarrow7\text{x}=5$
$\Rightarrow\text{x}=\frac{5}{7}$

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