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Old 22nd September 2012, 03:11 PM   #1 (permalink)
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A Maths Questions

Please help to me with these problwm:

1) Show that 3^loga = a^log3. Hence solve 2a^log3(3^loga) - 5a^log3 = 3.

2) Given that λ is the root of the equation 2x^2 = 3x-4, show that 4λ^3 = λ-12.

3. Given that 2^x+1.12^x = 3^1-2x, evluate 6^3x without the use of a calculator.

4a). In the expansion (1+3x)^n, where n is a positive constant, the ratio of the coefficents of x^2 to x is 15:2. Find the value of n.

b). Using the value of n found in (a), find the coefficient of x^2 in the expansion of (1+3x+3x^2)^6.

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Old 22nd September 2012, 03:16 PM   #2 (permalink)
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Re: A Maths Questions

For 1) since you have proven they are equal by putting lg on both sides, let the value of 3^loga = a^log3 be like x then use equation to solve it.

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Old 22nd September 2012, 04:40 PM   #3 (permalink)
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Re: A Maths Questions

2)
2x˛-3x+4
=(x-λ)(2x+b)
=2x˛-2λb+bx-λb

Solve for λ, hence prove the relation.

4)
Use binomial formula given in your formula list, and use unknowns of the 2 coefficient to solve.

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