I was wondering of thsee simplifications are possible, log4(y) =log2^2(y) =log2(y)^2 OR logy since.log2^2 is 1. Thank you.so.much!
Hello, Tutu!
Very imaginative thinking . . . sadly, it doesn't work.
I was wondering of thsee simplifications are possible:
. . $\displaystyle \log_4(y) \:=\:\log_{2^2}(y) \:=\:\log_2(y^2)\:\text{ or }\:\log_2(y)\:\text{ since }\log_22 \,=\,1.$
That last part is false: .$\displaystyle \log_2(y^2)$ does not equal $\displaystyle \log_2(y).$
And the first part is false; we cannot move the "2" like that.
Compare: .$\displaystyle \log_4(64) \,=\,3\:\text{ and }\:\log_2(64)\,=\6$