Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

How many numbers between 100 and 200 can be expressed as powers of 2? Show the steps you followed.

Which power of 2 is closest to 1000?Show your work

Sagot :

superkoopasirf
Let x = the number 2 must be raised to to make 100
Let y = the number 2 must be raised to to make 200

[tex]2^x = 100[/tex]
[tex]\log 2^x = \log 100[/tex]
[tex]x \log 2 = \log{100}[/tex]
[tex]x = \frac{\log 100}{\log 2} [/tex]
[tex]x \approx 6.64[/tex]

[tex]2^y = 200[/tex]
[tex]\log 2^y = \log 200[/tex]
[tex]y \log 2 = \log{200}[/tex]
[tex]y = \frac{\log 200}{\log 2} [/tex]
[tex]y \approx 7.64[/tex]

So the integer powers of 2 that would fall between 100 and 200 are between 6.64 and 7.64 - 7 is the only one.

Following a similar method for the second question:
Let z = the number 2 must be raised to to make 1000

[tex]2^z = 1000[/tex]
[tex]\log 2^z = \log 1000[/tex]
[tex]z \log 2 = \log 1000[/tex]
[tex]z = \frac{\log 1000}{\log 2} [/tex]
[tex]z \approx 9.97[/tex]

So [tex]2^{10}[/tex] is the closest power of 2 to 1000.
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.