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2 log(x + a) = log(16a^6) where a is a positive constant. How do I find x in terms of a?

The left hand side of the equation can be rewritten as log(x+a)^2, using the power rule for logs. We can then simplify log(x+a)^2=log(16a^6) to (x+a)^2=16a^6. Taking the square root of both sides, we find...

Answered by Emily V. • Maths tutor

13129 Views

How do I solve quadratic equation by completing the square : X^2 - 4X = 5

We have X² - 4X = 5, write the expression on the left side as X² - 2•2X = 5. Then we would need extra term 4 to complete the square, so adding 4 on the both sides gives us, X²

Answered by Rabin K. • Maths tutor

3388 Views

Integrate cos(4x)+16x^3 with respect to x

This is a simple integration, integrating each individual term with respect to x.For the cos(4x), you should use 'integration by substitution' as it is a function of a function.cos(4x) = cos(u) and u = 4x...

Answered by Aadil C. • Maths tutor

3187 Views

When calculating a question with a double integral question between two different ranges which range relates to which integration variable.

When doing double integration with two arbitrary variables, for example 'x' and 'y' look at the Integration on the inside and integrate the function between the given range. For example if the integrand i...

Answered by Piranavan V. • Maths tutor

2806 Views

How do I differentiate (e^(2x)+1)^3?

You might be tempted to start by expanding the brackets, but in this case it's much easier to use the chain rule. This is the rule that, to differentiate f(g(x)), we find f'(g(x))*g'(x). In other words, t...

Answered by Alfie H. • Maths tutor

3631 Views