Neco 2020 Mathematics Question 3

Practice essay / theory question 3 from the 2020 Neco Mathematics examination. This question covers Indices, Logarithms, Surds .

Neco 2020 Mathematics Essay / Theory

Topics: Indices Logarithms Surds

Question 3 NECO • 2020 • MATHEMATICS • essay

Consider the expression \(E = \frac{(2^{3x} \cdot 5^{2x-1})}{(10^{x+2})} \times (\sqrt{125})^{\,x}\).

( a )

Simplify \(E\) and write it in the form \(2^{a}\,5^{b}\) where \(a\) and \(b\) are expressed in terms of \(x\).

( b )

Given that \(E = 1\), determine the value of \(x\). (Give your answer in exact form and to three decimal places.)

( c )

Using the value of \(x\) found in part (b), evaluate \(\log_{2}\bigl(2^{4x}\,5^{2x}\bigr)\). (Give your answer to two decimal places.)

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This is Neco 2020 Mathematics Question 3. It is one of the essay questions from the 2020 Neco Mathematics examination.

The question covers Indices, Logarithms, Surds .

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