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Maths
A Level

Use logarithms to solve 9^x=15

According to the rules of logarithms, when you take a log of something to the power of something, you multiply the log of the base by the power, so in this case, taking logs of both sides would give us...

Answered by Molly B. Maths tutor
6250 Views

Integrate the following function by parts and reduce it to it's simplest form. f(x) = ln(x).

First note that ln(x) = 1ln(x), this is in the form udv/dx.

Let dv/dx = 1 and u = ln(x). 

du/dx = 1/x from the standard results and v = x by integration.

Answered by Ryan B. Maths tutor
4118 Views

Integrate sinx*ln(cosx) with respect to x.

1. ʃ sinx*ln(cosx) dx

First notice the composition ln(cosx). To make the expression easier to integrate we try substitution (substitution is often useful when trying to integrate expressi...

Answered by Darshan S. Maths tutor
16544 Views

How can we remember the difference between differentiation and integration?

Integration is the inverse of differentiation. I.e. for differentiation of linear expressions we multiply the coeifficient with the power of the unknown and then subract 1 from the power. Integration i...

Answered by Madeha N. Maths tutor
4194 Views

A curve has equation y = 4x + 1/(x^2) find dy/dx.

As in every case dy/dx can be found by differentiating each term individually with respect to x.

Let's first tackle the 4x term.

As always the ...

Answered by Callum H. Maths tutor
9092 Views

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