1.3: Logarithmic graph and equations

4PM1/1R/June/2022 — Question 7 · 11 marks

A curve C\displaystyle C has equation
y=log10(x+2).y=\mathrm{log}_{10}(x+2).
(a) Using the axes below, sketch the graph of C\displaystyle C. Label the coordinates of the points of intersection of C\displaystyle C with the coordinate axes.
(2)
(b) Solve the equation
2(loga4+loga16)=1.2\left(\mathrm{log}_a4+\mathrm{log}_a16\right)=1.
(3)
(c) Solve the equation
5logq16+4log2q=24.5\mathrm{log}_q16+4\mathrm{log}_2q=24.
(6)