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Given: log 5 = x and log 7 = y

August 27, 2026Mathematics

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Answer

1 - x + y

3 steps

The image provided for question 6.2 only states the given information: $\log 5 = x$ and $\log 7 = y$ . The actual question to be solved is missing.

Assuming the question asks to express $\log 14$ in terms of $x$ and $y$ :

Use logarithm properties to express $\log 14$ in terms of $\log 2$ and $\log 7$ .
$\log 14 = \log (2 \times 7)$ $= \log 2 + \log 7$
Express $\log 2$ in terms of $\log 5$ and $\log 10$ .
When no base is specified, it is assumed to be base 10, so $\log 10 = 1$ .
$\log 2 = \log \left(\frac{10}{5}\right)$ $= \log 10 - \log 5$ $= 1 - x$
Substitute the given values and the derived value into the expression for $\log 14$ .
$\log 14 = (1 - x) + y$ $= 1 - x + y$ $1 - x + y$

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