Solve. Round any solution the 4th decimal place

Question

5IN(m∧4) -4In(2m)=9

Answer 1

Fasten your seat belts on this one.

 

5ln(m^4) - 4ln(2m) = 9

 

5*4 ln(m) - 4(ln(2) + ln(m)) = 9                     Decomposing:  Laws of logarithms power and multiplication)

 

20 ln(m) - 4 ln(2) - 4 ln (m) = 9                      Simplifying and Distributive Property

 

16 ln(m) - 4 ln(2)                = 9                      Simplifying

 

16 ln(m)                             = 9 + 4Ln(2)        Isolating 16 ln(m)

 

ln(m)                                 = (9 + 4ln(2))/16  Isolating ln(m)

 

e ^ ((9 + 4ln(2))/16)         = m                      Converting to exponential form from log form

 

                  2.0871             = m                     Solve form m

 

Please check my work, I was in a bit of a hurry.

 

Cheers,

 

Alvin