The Student Room Group
Reply 1
RobbieC
log(2)x + 4log(x)2 = 5

where (y) indicates that y is the base.

I only got to
log(2)x + log(x)16 = 5

How do I finish!


Oh God, log(x)2 = 1/log(2)x, so u get:
log(2)x + 4/log(2)x = 5, then solve it, is it ok?
Reply 2
Yeah, I dont really like logarithms. They are sick. Thank you!
Reply 3
np, it's not so hard
Reply 4
Surely you know about change of base :cool:, don't you?

Well anyway, here's how you do it;

We say that logyx=(lnx/lny)

You have:

log2x+4logx2=5

(lnx/ln2)+4(ln2/lnx)=5

Let (lnx/ln2)=a => (ln2/lnx)=(1/a)

Let's form an equation in terms of a:

a+(4/a)=5

Multiply out by a:

(a^2)+4=5a

Therefore:

(a^2)-5a+4=0

Factorising gives:

(a-1)(a-4)=0

Therefore:

a=1 OR a=4

Therefore:

(lnx/ln2)=1

=> lnx=1(ln2)

=> x=2

OR

(lnx/ln2)=4

=> lnx=4(ln2)=(ln16)

=> x=16

Therefore:

x=2 OR x=16.

Newton.