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How to make four 7 s equal to 4 and to 10?

f(7, 7, 7, 7) = 1: 7/7 * 7/7 = 1
f(7, 7, 7, 7) = 2: 7/7 + 7/7 = 2
f(7, 7, 7, 7) = 3: (7+7+7)/7 = 3
f(7, 7, 7, 7) = 4: ?
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f(7, 7, 7, 7) = 10: ?
I can also make four 7s equal to 5, 6 , 7 , 8 and 9 by using square root and lg plus +, - * and / but not 4 and 10.

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    Unfortunately, puzzles tend to be swept away at this server (At least my experience with my puzzles). Hence, I decided to upvote it. – 2017-02-09
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    You shouldn't need to use logs for $5,6,7,8,9$, but $\sqrt{7\times7}=7$ is useful. – 2017-02-09
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    $$7+(7-7)\cdot 7=7$$ $$7-\frac{7+7}{7}=5$$ $$7+\frac{7+7}{7}=9$$ – 2017-02-09
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    $$\frac{7\cdot 7+7}{7}=8$$ $$\frac{7\cdot 7-7}{7}=6$$ – 2017-02-09
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    Stop asking the same question multiple times, please. – 2017-02-09
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    So, upto $10$ , we only need "+,-,*,/". We can reach $12$ as well : $\frac{77+7}{7}=12$. What about $11$ ? $\frac{77}{7}$ would work, but how can we use $4$ sevens ? – 2017-02-09
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    FWIW f(7,7,7,7) is both terrible and useless notation. – 2017-02-09

2 Answers 2

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$$\frac{77}{7}- 7=4$$

$$\frac{77-7}{7}=10$$

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    Just $\frac{77}{7}-7$ is easier for 4 – 2017-02-09
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    @Joffan I my god, didn't get this! I become old! – 2017-02-09
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How about this: $|\{7,7,7,7\}|=4$. Seems obvious but don't know if it falls in line with acceptable mathematical operations!

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    But $\{7, 7, 7, 7\}=\{7\}$ . . . – 2017-02-09
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    Here's a way to salvage the idea: $|\{7\}|+|\{7\}|+|\{7\}|+|\{7\}|=1+1+1+1=4$. – 2017-02-10
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    Quite right! The important lesson is to not answer posts late at night. Right idea but poorly executed - thanks for salvaging it @Theophile ! – 2017-02-10