Question

How do you solve `4(7^(x + 2)) = 9^(2x - 3)`?

Answer 1

`x=(-3ln(9)-2ln(7)-ln(4))/(ln(7)-2ln(9))`

Explanation:

you have to log the equations

`4*7^(x+2)=9^(2x-3)`

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

`ln(4*7^(x+2))=ln(9^(2x-3))`

First use the log rule that states `loga*b=loga+logb`

`ln(4)+ln(7^(x+2))=ln(9^(2x-3))`

Remember the log rule that states `logx^4=4logx`

`ln(4)+(x+2)ln(7)=(2x-3)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.