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Show that, for all a, b and c, a^log_b (c) = c^log_b (a).

We want to prove: a log b (c) = c log b (a) . Recall that we can always write x = e ln(x) , so x y = (e ln(x) ) y = e y ln(x) . Recall also the change of basis formula for logs: log b (x) = y <=> b y =...
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Answered by Tutor69809 D. • Maths tutor
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Sketch the curve y = x^2 - 6x + 5, identifying roots and minima/maxima.

Remeber the formula: (a - b) 2 = a 2 - 2ab + b 2 . Notice that y = x 2 - 2 3 x + 5, so we want to write this using (x - 3 ) 2 = x 2 - 2 3 x* + 9. Taking 4 from both sides gives: (x - 3) 2 - 4 = x 2 - 6x + 5 ...
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Answered by Tutor69809 D. • Maths tutor
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How would a reduction in interest rates lead to an increase in Economic Growth?

A reduction in interest rates would lead to a boost in Aggregate Demand and therefore an increase in real national output. If the monetary policy committee decide to reduce interest rates then the incentive ...
SC
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How can a fall in interest rates affect the Aggregate Demand of an economy

AD=C+I+G+(X-M) Interest rates (i) determine the return of saving money in a bank and the cost of borrowing money from a bank. Therefore, a fall in i means that the cost of borrowing falls and the return on s...
IK
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The demand curve can be graphed using the expression Q = 100 - P and the supply curve can be graphed using the expression Q = 40 + 2P. Find the equilibrium price and quantity in this market.

The equilibrium price and quantity within a market for a good can be found at the intersection of the supply and demand curves. Therefore, we need to use a mathematical method to find the P and Q by equating...
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Answered by Tamara K. • Economics tutor
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