GRADE 11- INDICES AND LOGARITHMS

GRADE 11- INDICES AND LOGARITHMS I

Index Laws

 $x^a\times x^b=x^{\left(a+b\right)}$ 

  $x^a\div x^b=x^{\left(a-b\right)}$  

 $\left(x^a\right)^b=x^{a\times b}$  

 $\frac{1}{x^a}=x^{\left(-a\right)}$  

 $x^0=1$  

Open Ended

Find the answer using logarithms   

 $\frac{45.89\times8.458}{589}$  

Open Ended

Find the answer using logarithms

 $\frac{0.5463\times58.22}{0.0046}$  

Open Ended

 $\sqrt{0.943}\times\left(0.745\right)^2\div7.834$ Find the value using logarithms 

Open Ended

A hemispherical container of radius r is completely filled with water. This water is poured into a glass container in the shape of a prism, having a triangular cross section with the measurements shown in the figure, such that no water spills out. Then the water fills this glass
container to a height of l0 cm. Show that the radius r of the hemispherical container is obtained by  $\ r=\ ^3\sqrt{\frac{180}{\pi}}$   (Cubic root of  $\frac{180}{\pi}$ )  and taking the value of  $\pi$   as 3.14, find the value of r in centimetres to the first decimal place.