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Solve the equation 3^(5x-2)=4^(6-x), and show that the solution can be written in the form log10(a)/log10(b).

So we have the equation initially in the form 3^(5x-2)=4^(6-x), and as the solution involves log10, then a sensible first move would be to take log10 of both sides, giving log10(3^(5x-2)) = log10(4^(6...

Answered by Eloise B. • Maths tutor

6337 Views

Prove that (sinx + cosx)^2 = 1 + 2sinxcosx

Starting on the left hand side we can expand out the brackets to get:
(sinx + cosx)(sinx + cosx)
sin²x+sinxcosx+sinxcosx+cos²x
Grouping together the like terms we can ...

Answered by Adam G. • Maths tutor

11904 Views

How do you integrate ln(x)?

Tricky. Definitely can't do it by inspection (we don't know any fuction that just differentaties to ln(x)), it's not like we've really got anything to substitute u for if we wanted to do it by substitu...

Answered by Ross G. • Maths tutor

99577 Views

Solve dy/dx= (x√(x^2+3))/e^2y given that y=0 when x=1, giving your answer in the form y = f(x)

The first thing we notice is that this differential equation is seperable, meaning we can get all of our y's on the left with a dy and all of our x's on the right with a dx. Doing this by multiplying b...

Answered by Ross G. • Maths tutor

12925 Views