Question
Solve for $\mathbf{x}: 4^{x-1} \times(0.5)^{3-2 x}=\left(\frac{1}{8}\right)^{-x}$
✓
Answer
$ 4^{x-1} \times(0.5)^{3-2 x}=\left(\frac{1}{8}\right)^{-x}$
$ \Rightarrow\left(2^2\right)^{x-1} \times\left(\frac{1}{2}\right)^{3-2 x}=\left(\frac{1}{2^3}\right)^{-x}$
$ \Rightarrow 2^{2 x-2} \times 2^{-(3-2 x)}=\left(2^{-3}\right)^{-x}$
$ \Rightarrow 2^{2 x-2-3+2 x}=2^{3 x}$
$ \Rightarrow 2^{4 x-5}=2^{3 x}$
$ \Rightarrow 4 x-5=3 x$
$ \Rightarrow 4 x-3 x=5$
$ \Rightarrow x=5$
$ \Rightarrow\left(2^2\right)^{x-1} \times\left(\frac{1}{2}\right)^{3-2 x}=\left(\frac{1}{2^3}\right)^{-x}$
$ \Rightarrow 2^{2 x-2} \times 2^{-(3-2 x)}=\left(2^{-3}\right)^{-x}$
$ \Rightarrow 2^{2 x-2-3+2 x}=2^{3 x}$
$ \Rightarrow 2^{4 x-5}=2^{3 x}$
$ \Rightarrow 4 x-5=3 x$
$ \Rightarrow 4 x-3 x=5$
$ \Rightarrow x=5$
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