Help with these two problems

Question

Write in exponential form: 8=1.40

 

Write in natural Logarithmic form ^3√e  =1.40

Answer 1

FIRST:  8=1.40 could be written 2³ = 2^log₂1.40

 

SECOND:  3√e =1.40 (given); take natural logs: ln 3 + ln√e = 1.40;  ln3 + ½ln e = ln 1.40;  ln 3 + ½ = ln 1.4;

 

ln 3 - ln 1.4 = ½;  ln (3/1.4) = ½   ⇐ THIS LOOKS LIKE A GOOD STOPPING POINT.

 

 

THERE IS SOME DOUBT ABOUT THIS PROBLEM BASED ON THE STRANGENESS OF THE ELEVATED LEFT SIDE, IN YOUR ORIGINAL PRESENTATION OF GIVEN THE EQUATION.