Question

logx​(2)+log2​(x)=0solveforx​

Answer 1

Answer:

First change the base on logx2 using the change of base identity:

logx2=log22/log2x=1/log2x

Then your equation becomes

log2x + 1/log2x =2.5

Let u=log2x and simplify:

u+1/u=2.5

u²-2.5u+1=0

 

Use the quadratic formula to solve this quadratic equation, get u = 2 or 1/2.

 

For u=2=log2x,  x=4.

For u=1/2=log2x, x=√2

Therefore, the two solutions are x=4 and x=√2

 

Check: log24 + log42 = 2+1/2=2.5

log2√2 + log √22 = 1/2 + 2 =2.5