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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 xlog9...
MB
Answered by Molly B. • Maths tutor
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Integrate the following function by parts and reduce it to it's simplest form. f(x) = ln(x).

First note that ln(x) = 1 ln(x), this is in the form u dv/dx. Let dv/dx = 1 and u = ln(x). du/dx = 1/x from the standard results and v = x by integration. Substituting into the formula integral(u dv/dx)dx = ...
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Answered by Ryan B. • Maths tutor
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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 expressions that are or incl...
DS
Answered by Darshan S. • Maths tutor
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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 is the ...
MN
Answered by Madeha N. • Maths tutor
5419 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 derivative can be found by multiplying the term by the power of ...
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Answered by Callum H. • Maths tutor
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