Question

Find x if logx 3+ log3 x =2.5

Answer 1

9 or
`√(3)`

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Use the following identity:

• 
  `log_a b=1/log_b a`

And show 2.5 as:

• 
  `2.5=2+(1/2)`

Now the equation is converted to:

• 
  `log_3x+(1/log_3x)=2+(1/2)`

Comparing both sides, we see that:

• 
  `log_3x=2`

or

• 
  `log_3x=1/2`

Find x:

• 
  `x=3^2=9`

or

• 
  `x=3^(1/2)=√(3)`