Proove the following

Question

(19)⁹³>(13)⁹⁹

Answer 1

19⁹³>13⁹⁹

 

ln(19⁹³)>ln(13⁹⁹)

 

93ln(19)>99ln(13)

 

ln(19)/ln(13)>99/93

 

ln(19-13)>99/93

 

ln(6)>1.0645

 

1.7917>1.0645

 

Statement is true

Answer 2

Take logarithms on both sides and compare them.  

 

Log₁₀(19⁹³)=93 x Log₁₀(19) which is approximately 274

Log₁₀(13⁹⁹)=99 x Log₁₀(13) which is approximately 253

 

if Log(a)>Log(b) then a>b