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Prove the change of base formula for logarithms. That is, prove that log_a (x) = log_b (x) / log_b (a).

Firstly, recall the definition of a logarithm: if y = log a (x), then this means that y is the power you have to raise a to, to get x, that is a y = x.Now, we want to introduce a new base, b. Let's take log ...
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Answered by Tom H. • Maths tutor
14177 Views

Outline the formation of hotspots and explain their relationship to plate movement.

Hotspots, which occur away from plate boundaries, develop when the decay of radioactive elements in the Earth's core heat magma directly above it in the mantle. The heated magma expands and becomes less dens...
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Answered by Sophie H. • Geography tutor
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How should I approach an unseen comparative analysis of two texts?

There are several skills that need to be demonstrated in order to create a strong comparative unseen essay. Firstly general competence in literary studies must be shown through good communication and knowled...
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How would I translate: De plus en plus nombreuses, les familles monoparentales sont aujourd’hui plus diverses, surtout parce que la société elle-même a évolué. Autrefois, être parent seul résultait avant tout du décès d’un époux.

First of all, it is important to get a sense of the meaning in its entirety, rather than launching straight into a translation. This will help you to translate it not word-for-word, which could sound clumsy,...
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Answered by Grace C. • French tutor
3103 Views

(ii) Prove by induction that, for all positive integers n, f(n) = 3^(3n–2) + 2^(3n+1) is divisible by 19

Let P(n) represent the statement that 'f(n) is divisible by 19'. For the basis step, I prove that P(1) is true: f(1) = 3 3(1)-2 + 2 3(1)+1 = 19. 19 is divisible by 19 so P(1) is true. I now want to prove tha...
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Answered by Daniel L. • Maths tutor
11019 Views