Additional Mathematics 4037: Logarithmic and exponential functions Topical Past Paper Questions

Two variables, x and y, are related by an equation of the form $ y = Ax^{b} $, where A and b are constants. The following pairs of values of x and y are given. (a) On the axes below, use these values to draw the straight-line graph of $ \ln y $ against $ \ln x $. [2] [2]

Solve the following equations. (a) $ \log_{2}x^{2}+\log_{16}x=18 $ [4] (b) $ \mathrm{e}^{2x+1}-10\mathrm{e}^{-2x-1}=3 $ [4]

(a) Solve the following simultaneous equations. $$ \begin{aligned}&3\log_{2}x+2\log_{2}y=24\\&5\log_{2}x-3\log_{2}y=2\\ \end{aligned} $$ (b) Solve the equation $ \frac{2^{t+4}}{2^{1-2t}}=512 $. [5]