If `log (0.57) = 0. 756` then the value of `log 57 + log (0.57)^(3) + log sqrt(0.57)`` (-9)/(2)` is :

Options

A. 0.902
B. 1.902
C. 1.146
D. 2.146

Answer

To solve the problem, we will use the properties of logarithms. Let's break it down step by step.

### Step 1: Rewrite the expression
We start with the expression we need to evaluate:

\[ \log 57 + \log (0.57)^3 + \log \sqrt{0.57}^{-9/2} \]

Using the property of logarithms that states \(\log a + \log b = \log(ab)\), we can combine the logarithms:

\[ \log(57 \cdot (0.57)^3 \cdot \sqrt{0.57}^{-9/2}) \]