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# Given that log107 = x and log102 = y, evaluate without using tables, log1035...

### Question

Given that log107 = x and log102 = y, evaluate without using tables, log1035

### Options

A) x + y

B) x - y + 1

C) $$\frac{(x + 1)}{y}$$

D) x - y

### Explanation:

$$\log_{10} 7 = x$$ and $$\log_{10} 2 = y$$
$$\log_{10} 35 = \log_{10}(\frac{70}{2}) = \log_{10} 70 - \log_{10} 2$$
$$\log_{10}(7 \times 10) - \log_{10}2$$
$$\log_{10} 7 + \log_{10} 10 - \log_{10} 2$$
$$= x + 1 - y = x - y + 1$$

## Dicussion (1)

• $$\log_{10} 7 = x$$ and $$\log_{10} 2 = y$$
$$\log_{10} 35 = \log_{10}(\frac{70}{2}) = \log_{10} 70 - \log_{10} 2$$
$$\log_{10}(7 \times 10) - \log_{10}2$$
$$\log_{10} 7 + \log_{10} 10 - \log_{10} 2$$
$$= x + 1 - y = x - y + 1$$