SOLUTION: (Solving Natural Logarithms to solve Exponential Equations)Give an exact answer and then an answer rounded to the nearest thousandth.
Problem:
3^x-1=4^2x+3
Question 585261: (Solving Natural Logarithms to solve Exponential Equations)Give an exact answer and then an answer rounded to the nearest thousandth.
Problem:
3^x-1=4^2x+3 Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! 3^(x-1)=4^(2x+3)
take ln of both sides:
ln(3^(x-1)) = ln(4^(2x+3))
(x-1)ln(3) = (2x+3)ln(4)
xln(3)-ln(3) = (2x)ln(4)+3ln(4)
xln(3) = (2x)ln(4)+3ln(4)+ln(3)
xln(3)-(2x)ln(4) = 3ln(4)+ln(3)
x(ln(3)-(2)ln(4)) = 3ln(4)+ln(3)
x = (3ln(4)+ln(3))/(ln(3)-(2)ln(4)) exact
x = -3.141
