Calculate Expression for e from c and d

[thomas49th]

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?

 

[HallsofIvy]

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 4^d= (2²)^d= 2^2d. 8= 2³ so 8^e= (2³)^e= 2^3e.

 

[thomas49th]

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?

 

[HallsofIvy]

That was a typo. I have corrected it.