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How do I solve the following question. 'Find the values of x such that 2log3(x) - log3(x-2) = 2'.

How do I solve the following question. 'Find the values of x such that 2log 3 (x) - log 3 (x-2) = 2'.To simplify this equation in order to solve it, the first step is to simplify the 2log 3 x term. The log r...
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Answered by Lauren R. • Maths tutor
17702 Views

How does integration by parts work?

The method of integration by parts is working upon the Product Rule in differentiation. We know the Product Rule to be d/dt (uv) = uv' + vu', where u and v are separate functions and u' and v' are the corres...
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Answered by Finn I. • Maths tutor
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Solve algebraically the following system of equations: 4x + 5y = -3; 6x - 2y = 5

To solve these algebraically, we need to eliminate one of the two variables (either x or y) and solve for the remaining variable. We then substitute the answer found into one of the two given equations to fi...
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Answered by Cara S. • Maths tutor
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Solve algebraically the simultaneous equations x^2 +y^2 = 25, y – 3x = 13

Rearrange y - 3x = 13y = 3x + 13 2. Substitute into x^2 +y^2 = 25x^2 + (3x + 13)^2 = 25 3. Expand bracketx^2 +(9x^2 + 39x +39x +169) = 25 4. Form quadratic equation 10x^2 + 78x + 144 = 0 (Dividing by 2 makes...
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Answered by Emily N. • Maths tutor
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There are 5 girls, 6 boys and some adults in a classroom. The probability that a girl is chosen is 1/3. What is the probability of an adult being chosen?

This is a question taken straight out of an Edexcel exam paper. I think it's a good test of GCSE level probability and algebra. We don't know how many adults there are to begin with so let's say n = number o...
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Answered by Jack M. • Maths tutor
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