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OCR C2 2015 Question 8: (a) Use logarithms to solve the equation 2^(n-3) = 18,000 , giving your answer correct to 3 significant figures. (b) Solve the simultaneous equations log2(x) + log2(y) = 8 & log2(x^2/y) = 7.

(a) This question actually tells us what to do . It is very hard to miss " use logarithms to solve... ". So our first step is going to be to use logs (especially as we can also see that is very lit...
JH
Answered by Jonathan H. • Maths tutor
8090 Views

How do you integrate sin(3x)cos(5x)?

STEP 1 Cannot integrate directly in this form, therefore use a trigonometric identity. Identity: sin(A) + sin(B) = 2sin((A+B)/2)cos((A-B)/2) STEP 2 (A+B)/2 = 3x A + B = 6x (1) (A-B)/2 = 5x A - B = 10x (2) ST...
CF
Answered by Catherine F. • Maths tutor
8770 Views

Why does the constant disappear when differentiating a function?

We can think of the constant term in a function in terms of x, for example in x^2 + 3x + 2 as 2 being multiplied by x^0. Anything to the power of 0 is equal to one, so in our example we would have 2 * x^ 0 w...
AP
Answered by Abdullah P. • Maths tutor
13320 Views

Factorise: y = x^2 + 5x + 6

With quadratic equations, there are two ways in which to answer Firstly (and most simply), look for two numbers that multiply to make c and add up to make b in the equation y = ax 2 + bx + c , so in the exam...
AN
Answered by Adnan N. • Maths tutor
6170 Views

Can you show me why the integral of 1/x is the natural log of x?

We can break this down into steps, going deeper each time. First we might just say: well, since integration is fundamentally the inverse process of differentiation and we know that the derivative of ln(x) is...
JL
Answered by James L. • Maths tutor
10936 Views