The problem is to evaluate the expression $\sqrt{8357} \times 0.895^2$ using logarithms. The steps provided in the image appear to calculate $\log(\sqrt{8357} \times 0.895^2)$ and then try to find the antilogarithm.

1. Problem Description

The problem is to evaluate the expression $\sqrt{8357} \times 0.895^2$ using logarithms. The steps provided in the image appear to calculate $\log(\sqrt{8357} \times 0.895^2)$ and then try to find the antilogarithm.

2. Solution Steps

First, we can write the logarithm of the expression as:

$$\log(\sqrt{8357} \times 0.895^2) = \log(\sqrt{8357}) + \log(0.895^2)$$

$$= \log(8357^{1/2}) + \log(0.895^2)$$

Using the logarithm power rule, $\log(a^b) = b\log(a)$:

$$= \frac{1}{2}\log(8357) + 2\log(0.895)$$

From the image, we have $\log(8.357) \approx 0.9221$. Therefore $\log(8357) = \log(8.357 \times 10^3) = \log(8.357) + \log(10^3) = 0.9221 + 3 = 3.9221$.

And $\log(0.895) \approx -0.0486$. This is written as $\bar{1}.9518$ in the image, which means $-1 + 0.9518 = -0.0482$.

Note that the image indicates $\log(0.895) = \bar{1}.9518$, where $\bar{1}$ denotes -

1. Therefore, $2 \times \bar{1}.9518 = \bar{2}.9036$ and $\frac{1}{2} \times 3.9221 = 1.96105 \approx 1.9611$.

So, $\frac{1}{2}\log(8357) + 2\log(0.895) = \frac{1}{2} (3.9221) + 2(\bar{1}.9518) = 1.96105 + \bar{2}.9036 = 1.96105 - 2 + 0.9036 = 0.86465$.

Then, we have

$$\log(\sqrt{8357} \times 0.895^2) \approx 1.9611 + (-0.0482 \times 2) = 1.9611 - 0.0964 = 1.8647$$

Taking the antilogarithm (base 10):

$$10^{0.8647} \times 10 = 10^{1.8647} \approx 73.23$$

According to the image, $\log(n) = 0.3647$, therefore $n=2.316$.

However, the actual calculation of $\sqrt{8357} \times 0.895^2 = \sqrt{8357} \times 0.801025 \approx 91.4166 \times 0.801025 \approx 73.2226$.

Given values in the image: $\frac{1}{2}*0.9221 + 2*\bar{1}.9518 = 0.4611 + \bar{1}.9036 = 0.4611 - 1 + 0.9036 = 0.3647$

If $0.3647$ is the result of logarithm, then $10^{0.3647} = 2.316$. Thus, $n = 2.316$.

3. Final Answer

2. 316