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a) Using log rules, a^x=b becomes log(a)b=x. If we take ln of both sides, we get ln(e^(3x-9))=ln8. ln(e) =1, so we just get 3x-9=ln8. Now we can simply manipulate this to get x=(9+ln8)/3=3+(1/3)ln8. Anoth...

Start with a). Looking at this equation, the trig identity screaming out is cosx^2+sinx^2=1--> cosx^2=1-sinx^2. Substituting this into the LHS of the equation, and with a bit of algebraic rearrangement...

The key to solving simultaneous equations is trying to reduce them into one equation. You can see that one of these equations is quadratic, so you should be thinking there will be 2 answers for x and y. Y...

eq.1 4x+3y=7eq.2 3x+7y=16You want to eliminate one of the variables (either x or y) reducing the problem to just one equation with one variable which can be solved. This can be done by multiplying e...

First it is important to identify that this is an integration by parts question as it can't be solved by substitution. Let I = integral for ease of notation.Write out integration by parts formula I(...