Logarithms, Indices & Exponentials (Edexcel IGCSE Further Pure Maths): Exam Questions

Solve the equation ${\log }_{2}x+6{\log }_{x}2=7$

Find the value of $a$ such that ${\log }_{a}8=\frac{3}{4}$

Show that

$3x{\log }_{2}x-4{\log }_{16}8+6x{\log }_{4}8-{\log }_{2}x={\log }_2{\left(8x\right)}^{3x-1}$

Hence solve the equation $3x{\log }_{2}x-4{\log }_{16}8+6x{\log }_{4}8-{\log }_{2}x=0$

Solve the equation $5\left({\log }_{b}9+{\log }_{b}3\right)=3$

Solve the equation $3{\log }_{3}x+3{\log }_{x}27=8{\log }_{4}128$
Give your answers in exact form.

Solve the equation

${\log }_2{x}^3+{\log }_4{x}^2-3{\log }_{x}2=0$

giving your answers to 3 significant figures.

Solve the simultaneous equations

$$\begin{gathered} 2{\log }_{4}x={\log }_{3}3y^2 \\ {\log }_2{x}^3+8{\log }_{9}y=13 \end{gathered}$$

Show your working clearly.

Complete the table of values for

$y=0.5^{\left(\frac{x}{3}+1\right)}+2$

giving each value to 2 decimal places where appropriate.

On the grid opposite, draw the graph of $y=0.5^{\left(\frac{x}{3}+1\right)}+2$ for $-6⩽x⩽0$

By drawing a suitable straight line on the grid, obtain an estimate, to one decimal place, of the root of the equation

${\log }_2(2x+2{)}^3+x+3=0$ in the interval $-6⩽x⩽0$

Giving each value in your solution to 2 decimal places, solve the simultaneous equations

$$\begin{gathered} e^{2y}-x+2=0 \\ \ln (x+3)-2y-1=0 \end{gathered}$$