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Compare the following logarithms in base 1/2 without a calculator: log(8) and log(512)

Compare through subtraction : log 0.5 (8)- log 0.5 (512) = xUsing logarithm rule in addition/subtraction: log a (b)+log a (c) = log a (b*c) ; log a (b)-log a (c) = log a (b/c) where a,b and c are constants (...
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Answered by Gael A. • Maths tutor
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y=7-2x^5. What's dy/dx?Find an equation for the tangent to the curve where x=1. Is itan increasing or decreasing function when x=-2?

dy/dx=-10x^4When x-1, gradient =-10 Tangent is then: y+10x=15When x=-2, dy/dx=-160 so a decreasing function
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Answered by Khai L. • Maths tutor
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Factorise the following: 21x(squared)-35x

The question is asking us to factorise, this means put the equation into a simplified bracket. The first step is to find the highest common factor (HCF), the HCF must be a factor of 21x 2 as well as -35x. I ...
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Answered by Annesa M. • Maths tutor
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simplify fully (x^2-5x+4)/(x^2-2x-8)

First we need to look at the quadratic formulas separately and factorise them. (x^2-5x+4) the sum is -5 and the product is 4, we need to find numbers that add to get -5 and multiply to get 4, which is -4, an...
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Answered by Aisling H. • Maths tutor
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work out 2/15 x 15/22

When multiplying fractions you multiply the numerators together to get the resulting numerator, and multiply the denominators to get the denominator. In this case you would have (2/15 x 15/22) when written n...
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Answered by Aisling H. • Maths tutor
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