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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

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 = a² - 2ab + b². Notice that y = x² - 23x + 5, so we want to write this using (x - 3)

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 incenti...

Answered by Sebastian C. • Economics tutor

2014 Views

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 o...

Answered by Isabella K. • Economics tutor

7292 Views

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 equat...

Answered by Tamara K. • Economics tutor

2256 Views