Help me with this sum: Admiss a filter that let pass 4/5 of the light's intensity

[dweera]

For better studying the sun, astronomies use light filters on your observation instruments. Admiss a filter that let pass 4/5 of the light's intensity that affects it. For reducing this intensity in less than 10% from original, it was necessary to use "n" filters.
Whereas log2=0.301, the less "n"'s value is:

A- 9
B- 10
C- 11
D- 12

 

[HallsofIvy]

"Admiss"? If one filter "lets pass 4/5 of the sun's light", two filters would pass 4/5 of 4/5= 16/25= 0.64 of the suns light. Three filters would pass 4/5 of 16/5= 64/125= 0.52 of the suns light. How many do you need to get below 0.10? There are two ways of doing this. One is just keep doing the calculation above, until you get a number less than 0.10. The other is to solve \(\displaystyle \left(\frac{4}{5}\right)^n< 0.10\) and determine the smallest integer value for n.