Question

1+2log2 base x*log(10-x) base 4=2/log x base 4​

Answer 1

Some of the basic results used here:

logab=logcblogcaloga⁡b=logc⁡blogc⁡a

logax=y⟹x=ayloga⁡x=y⟹x=ay

logab=blogalog⁡ab=blog⁡a

Now focusing on the problem,

log2x+log4x=2log2⁡x+log4⁡x=2

∴logxlog2+logxlog4=2∴log⁡xlog⁡2+log⁡xlog⁡4=2

∴logxlog2+logx2log2=2∴log⁡xlog⁡2+log⁡x2log⁡2=2

∴logxlog2(1+12)=2∴log⁡xlog⁡2(1+12)=2

∴32×logxlog2=2∴32×log⁡xlog⁡2=2

∴log2x=43∴log2⁡x=43

∴x=2

Answer 2

2 or 8

here the answer is in picture I hope you like it