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First take natural logs of both sides, giving us: ln(3^x * e^4x) = ln(e⁷).  The RHS can be simplified using the definition of natural logs, so ln(e⁷) = 7.

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A key example of a poet expressing change comes in Carol Ann Duffy's 'Originally' from her 1990 collection The Other Country. In the poem, Duffy utilises imagery such as that of the turn...

An accent is commonly associated with sounds of a particular variety, so pronunciation. A dialect is commonly associated with the lexis and grammar of a variety e.g. the non-standard 'I were' in some Manc...

For the first part, use the 'complete the square method', which gives (x-7/2)² -49/4+2, simplified to (x-7/2)²-41/4. To find the answer for the second part, set x=7/2 so that the bra...

This is a good example of where simplification can make an otherwise tricky question a lot easier. It is easy to get confused trying to work out different isotopes and the extra products of the decays, bu...