Calculate Expression for e from c and d

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To express e in terms of c and d from the equation 2^{c}4^{d} = 8^{e}, first rewrite 4 and 8 in terms of base 2: 4 is 2^2 and 8 is 2^3. This transforms the equation into 2^{c} * (2^{2})^{d} = (2^{3})^{e}, simplifying to 2^{c + 2d} = 2^{3e}. By equating the exponents, c + 2d = 3e can be derived. Finally, solving for e gives e = (c + 2d)/3.
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Express e in terms of c and d if 2^{c}4^{d} = 8^{e}

Can someone give me step by step advice on how to answer this?
 
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thomas49th said:
Express e in terms of c and d if 2^{c}4^{d} = 8^{e}

Can someone give me step by step advice on how to answer this?
4= 22 so 4d= (22)d= 22d. 8= 23 so 8e= (23)e= 23e.
 
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I don't get

(2^{3})^{e}= 3^{3e}

I see that 2³ = 8 and (^{e})^{3} is ^{3e}, but how can that be 3^{3e}
?



P.S Can i ask, the dot in the middle of a line, is it suppost to represent a new equaion?
 
That was a typo. I have corrected it.
 

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