Using the fact that loga(an) = n, we have: log22 + log2(22) + log2(23) + ... + log2(218) = 1+2+3+...+18 = 171
Roheena N.
asked • 07/16/21Exponential & Log Functions
Evaluate, using the properties of log.
log2 2 + log2 4 + log28 +⋯+ log2262144.
Follow
•
1
Add comment
More
Report
2 Answers By Expert Tutors
Raymond B. answered • 07/16/21
Tutor
5
(2)
Math, microeconomics or criminal justice
loga + logb = logab
loga + logb + logc = logabc
log2 + log4 + log8 + log16 + log32 + log64 + log128 + log 256 + log512 + log 1024 + log 2048 + log4096 + log 8192 + log 16384 = log 32768 + log 65536 + log 131072 + log 262144
= log(2)(4)8(16)(32)(64)(128)256(512)(1024)(2048)(4096(8192)16384(32768)(65536)(131072)(262144)
= log(3.624524061 x 10^48)
ln(3.6 x 10^48) = about 22.6
use change of base formula to convert to base 2
logba = lna/lnb with b=2 and a = (3.6 x10^48)
log2(3.6 x10^48) = 22.6/ln2 = about 32.6
Still looking for help? Get the right answer, fast.
Ask a question for free
Get a free answer to a quick problem.
Most questions answered within 4 hours.
OR
Find an Online Tutor Now
Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.
