SOLUTION: 1)solve exactly for x when 12e^(0.03x)=15e^(0.01x) 2)solve exactly for x when 4^(ln(3x+2))=13

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 1)solve exactly for x when 12e^(0.03x)=15e^(0.01x) 2)solve exactly for x when 4^(ln(3x+2))=13      Log On


   

Question 515626: 1)solve exactly for x when 12e^(0.03x)=15e^(0.01x)
2)solve exactly for x when 4^(ln(3x+2))=13
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
1)solve exactly for x when 12e^(0.03x)=15e^(0.01x)
2)solve exactly for x when 4^(ln(3x+2))=13
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1) 12e^(0.03x)=15e^(0.01x)
ln12+.03x*lne=ln15+.01x*lne
lne=1
ln12+.03x=ln15+.01x
.02x=ln15-ln12
x=(ln15-ln12)/.02=11.1572
..
2) 4^(ln(3x+2))=13
ln(3x+2)*ln4=ln13
ln(3x+2)=ln13/ln4=1.8502
Convert to exponential form: base(e) raised to log of number(1.8502)=number(3x+2)
e^1.8502=3x+2
6.3611=3x+2
3x=4.3611
x=4.3611/3=1.4537