How do you solve 4(7x+2)=92x3?

1 Answer
Apr 22, 2018

x=3ln(9)2ln(7)ln(4)ln(7)2ln(9)

Explanation:

you have to log the equations

47x+2=92x3

Use either natural logs or normal logs ln or log and log both sides

ln(47x+2)=ln(92x3)

First use the log rule that states logab=loga+logb

ln(4)+ln(7x+2)=ln(92x3)

Remember the log rule that states logx4=4logx

ln(4)+(x+2)ln(7)=(2x3)ln(9)

ln(4)+xln(7)+2ln(7)=2xln(9)3ln(9)

Bring all the xln terms to one side

xln(7)2xln(9)=3ln(9)2ln(7)ln(4)

Factorise the x out

x(ln(7)2ln(9))=(3ln(9)2ln(7)ln(4))

x=3ln(9)2ln(7)ln(4)ln(7)2ln(9)

Solve on the calculator using the ln button or if your calculator doesn't have it use the log base 10 button.