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Question

The value of $$\displaystyle \log_{4}8 = \cfrac 3m$$. The value of $$m$$ is: 


Solution

Let $$x =\displaystyle \log_{4}8$$
$$\displaystyle \Rightarrow 4^{x}=8$$
$$\displaystyle \Rightarrow 2^{2x}=2^{3}$$
$$\Rightarrow 2x=3$$
$$\displaystyle \Rightarrow x= \cfrac 32$$
Hence, $$m=2$$       

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