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In this question, take 'log' to mean 'log base 5'. Solve the equation log(x^2-5)-log(x) = 2*log(2)

Note that you can not take a positive base log of a negative number. log 5 (x 2 -5) - log 5 (x) = 2log 5 (2) => log 5 ((x 2 -5)/x) = log 5 (4) => (x 2 -5)/x = 4 => x 2 - 4x - 5 = 0 => x = -1 or 5...
ML
Answered by Milan L. • Maths tutor
4197 Views

What is the difference between 'J'aimerais de nouvelles chaussures' and 'Jaimerais les nouvelles chaussures' ?

Articles always seem tricky in French, but with practice they are simple! In the first example the indefinite article 'des' is used - this means that the sentence is talking about new shoes in general. In co...
SL
Answered by Shereen L. • French tutor
3778 Views

Solve the

5
ML
Answered by Milan L. • Maths tutor
3955 Views

Find dy/dx such that y=(e^x)(3x+1)^2.

We will solve this question with the knowledge that dy/dx = u.(dv/dx) + v.(du/dx), where y=u.v We have y=e^x(3x+1)^2. First, we want to find u & v. By splitting the function, we have that u=e^x and v=(3x...
SB
Answered by Stefanie B. • Maths tutor
4925 Views

Show that 2tan(th) / (1+tan^2(th)) = sin(2th), where th = theta

We have 2tan(th) / (1 + tan^2(th)) = sin(2th) We know that tan(A) = sin(A) / cos(A), and 1 + tan^2(A) = sec^2(A) Therefore => (2sin(th) / cos(th)) / sec^2(th) => 2sin(th)*cos^2(th) / cos(th) => 2sin...
IC
Answered by Ian C. • Maths tutor
4226 Views