lnx^3- 2lnx=1 solve for x.

Question

ln x^3- 2lnx=1 solve for x.

Answer 1

Niloufar,

 

Recall that ln(x³) = 3 ln(x)  and working in reverse that 2ln(x) = ln(x²).  So you have 2 quick ways of solving your equation:

 

(1) Simplify the first term 

 

ln(x³) - 2ln(x) = 1

3ln(x) - 2ln(x) = 1

ln(x) = 1 ,  then take the exponent of both sides  

e^ln(x) = e¹  so x = e¹ = e = 2.718...

 

Or (2) Rewrite the second term instead

 

ln(x³) - ln(x²) = 1  

ln(x³ / x²) = ln(x) = 1 and x = e once again.