How do you solve 2^3x = 3e^x ? Thanks

2 Answers
Jan 4, 2018

~=1.02

Explanation:

2^(3x)=3e^x

ln2^(3x)=ln(3e^x)

3xln2=ln3+lne^x

3x*0.69314718056=1.09861228867+x

2.07944154168x-x=1.09861228867

1.07944154168x=1.09861228867

x=1.09861228867/1.07944154168

1.01775987513 ~=1.02

NOTES: lnx is "1-1" so you can plug it in the equation.

  • ln(ab)=lna+lnb
  • lna^x=xlna
  • lne=1
Jan 4, 2018

x=1.018

Explanation:

2^(3x) = 3e^x

ln2^(3x) = color(red)(ln(3e^x)

x*ln2^(3) -color(red)(x*ln(3e))=0

x(ln2^(3) -ln(3e))=0

x=0/(ln2^(3) -ln(3e))=0

Watch out for that step highlighted by red color. It's common mistake. correct version:

ln2^(3x) = ln(3e^x)

ln2^(3x) = lne^x+ln3

x*ln2^(3)- x*lne=ln3

x(ln2^(3)-lne)=ln3

x=ln3/(ln2^(3)-lne)=1.018