Solving Logarithmic Equation: Why Isn't It Working?

[tweety1234]

Homework Statement

I can't seem to get my head round this problem, I know how to use the 'change the base rule'

log_2 x + log_4x = 2

\frac{logx}{log2} + \frac{logx}{log4} = 2

why is this not correct ??

 

[mgb_phys]

It looks correct - what's the problem
(of course everytime I stray into maths I make an dumb mistake!)

 

[tweety1234]

It looks correct - what's the problem
(of course everytime I stray into maths I make an dumb mistake!)

well the answer book gives the solution like this,

log_2x + \frac{log_2 x}{log_2 4} = 2 don't understand why its base 2 here?

log_2 x + \frac{log_2 x}{2} =2

\frac{3}{2}log_2 x = 2 don't understand were 3/2 came from ?

log_2 x = \frac{4}{3}

x = 2^{\frac{4}{3} }

 

[mgb_phys]

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

 

[tweety1234]

log_2 x + log_4x = 2

\frac{logx}{log2} + \frac{logx}{log4} = 2

so is this method still correct? can I just add both logs up ?

 

[mgb_phys]

Except you are trying to find X so first you have to multiply out log(2) and log(4)

 

[tweety1234]

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

sorry, I still don't get where 1.5 comes from ? I thought you just multiply both sides by two to get rid of the fraction ?

2log_2 x + log_2 x = 4

 

[mgb_phys]

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

 

[tweety1234]

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

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

oh I get it now, thanks a lot for your help!