Discussion Forum

If $log(0.57)$ $=\overline{1}$$.756$, then the value of log 57 + log $(0.57)^{3}$ + log $\sqrt{0.57}$ is :

Answer:

Explanation:

$log(0.57)$ $=\overline{1}$$.756$

$\Rightarrow$ log 57 = 1.756   $\because$ [mantissa will remain the same].

$\therefore$ log 57 + log $(0.57)^{3}$ + log $\sqrt{0.57}$

= log 57 +3log $\left(\frac{57}{100}\right)$ + log $\left(\frac{57}{100}\right)^{1/2}$

= log 57 + 3log 57 - 3log 100 + $\frac{1}{2}$log 57 - $\frac{1}{2}$log 100

$=\frac{9}{2}$log 57 - $\frac{7}{2}$log 100

$=\frac{9}{2}\times 1.756$ $-\frac{7}{2}\times 2$

$=7.902-7$ = 0.902.