The discussion revolves around solving a logarithmic equation involving different bases, specifically the equation log_2 x + log_4 x = 2. Participants are exploring the application of the change of base rule and the implications of converting logarithms to a common base.
Some participants have provided insights into the simplification process, noting that combining logarithms into a single base can clarify the solution. However, there remains some uncertainty about specific steps and the reasoning behind certain transformations.
Participants express concerns about potential mistakes in their calculations and the interpretation of logarithmic properties. There is an ongoing exploration of how to manipulate logarithmic expressions correctly without losing track of the original equation.
mgb_phys said:It looks correct - what's the problem
(of course everytime I stray into maths I make an dumb mistake!)
tweety1234 said:log_2 x + log_4x = 2
\frac{logx}{log2} + \frac{logx}{log4} = 2
mgb_phys said:They are just collapsing it all into the same base log.
log_2 x + \frac{log_2 x}{2} =2 is just
1.5 * log_2 x =2 which is
\frac{3}{2} * log_2 x =2
It's the same answer as you get - but you can do it this way without needing to calculate log() of anything
mgb_phys said:They are just collapsing it all into the same base log.
log_2 x + \frac{log_2 x}{2} =2 is just
1.5 * log_2 x =2 which is
\frac{3}{2} * log_2 x =2
It's the same answer as you get - but you can do it this way without needing to calculate log() of anything
mgb_phys said:log_2 x + \frac{log_2 x}{2} = 2
Which if you ignore the logs for now is just; a + a/2 = 2
a(1+1/2) = 2
1.5a = 2
3/2 a =2