Compare the following logarithms in base 1/2 without a calculator: log(8) and log(512)

Compare through subtraction : log0.5(8)- log0.5(512) = xUsing logarithm rule in addition/subtraction: loga (b)+loga(c) = loga(b*c) ; loga (b)-loga(c) = loga(b/c) where a,b and c are constants (note both logarithms need to have same base 'a' for this rule to apply)
We get: log0.5(8)- log0.5(512) = log0.5(8/512) = log0.5(1/64)Using the logarithm properties: -loga(1) = 0 for any base 'a' -if base a < 1 the logarithmic function is strictly decreasing if base a > 1 the logarithmic function is strictly increasing
In our case, the base a = 1/2 is inferior to 1, this means the logarithm will be positive for x < 1 and negative for x > 1.We have 1/64 < 1 which implies log0.5(1/64) > 0.Hence :log0.5(8) - log0.5(512) > 0And finally:log0.5(8) > log0.5(512)

GA
Answered by Gael A. Maths tutor

2687 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A curve has equation y=2x^3. Find dy/dx.


By completing the square, find the values of x that satisfy x^4 -8x^2 +15 = 0


Let X be a normally distributed random variable with mean 20 and standard deviation 6. Find: a) P(X < 27); and b) the value of x such that P(X < x) = 0.3015.


(A-Level) Find the coordinate of the stationary point of the curve y = 2x + 27/x^2


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences