Home » Mathematics Theory (a)(i) Given that (log_{10} 5 = 0.699) and (log_{10} 3 = 0.477), find (log_{10} 45),…

Mathematics Theory (a)(i) Given that (log_{10} 5 = 0.699) and (log_{10} 3 = 0.477), find (log_{10} 45),…

(a)(i) Given that (log_{10} 5 = 0.699) and (log_{10} 3 = 0.477), find (log_{10} 45), without using Mathematical tables.

(ii) Hence, solve (x^{0.8265} = 45).

(b) Use Mathematical tables to evaluate (sqrt{frac{2.067}{0.0348 times 0.538}})

Explanation

(a)(i) (log_{10} 45 = log_{10} (3 times 3 times 5))

= (log_{10} (3^{2} times 5))

= (log_{10} 3^{2} + log_{10} 5)

= (2 log_{10} 3 + log_{10} 5)

= (2(0.477) + 0.699)

= (0.954 + 0.699 = 1.653)

(ii) (x^{0.8265} = 45)

Taking the log of both sides,

(log_{10} x^{0.8265} = log_{10} 45)

(0.8265 log_{10} x = log_{10} 45)

(log_{10} x = frac{1.653}{0.8265})

(log_{10} x = 2)

(x = 10^{2} = 100)

(b) (sqrt{frac{2.067}{0.0348 times 0.538}})

No Log
2.067 (0.0348)       = 0.3513 –
0.0348

(bar{2}.5416 +)

0.538 (bar{1}.7308)
  (bar{2}.2724) = (bar{2}.2724)
                           = (2.0789 div 2 = 1.0395)
Antilog – 10.95  

(therefore sqrt{frac{2.067}{0.0348 times 0.538}} = 10.95)