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Surely you know about change of base , 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.

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.

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