Given that a and b are positive constants, solve the simultaneous equations a = 3b, log 3 a + log 3 b = 2. Give your answers as exact numbers.
- first, write out given equations a = 3b and log3a + log3b = 2
2) substitute in the first equation into the second log33b + log3b = 2
3) simplify using log rules: log33b2 = 2
4) expand out the logarithms: 9 = 3b2
5) simplify and solve the equation for b: 3 =b2 so:
b = sqrt3 and b= - sqrt3
6) Now that you know b, you can substitute it back into the original equation to find a.
We know that, a = 3b so a =3sqrt3. and a= -3qsrt3
In summary, this question required knowledge of three key areas: 1) what a log is 2) log rules 3) how to solve simultaneous equations. As you can see, knowing these three things, you can solve any question of this format!
