Verified Answer :

SenpaiTrill

Hello there.

Which of the following is equivalent to log750 rounded to three decimal places?

1.772

Answer:

option (a) is correct.

\(\log_7 (50)=2.010\)

Step-by-step explanation:

Given : \(\log_7{50}\)

We have to chose out of given options that is equivalent to \(\log_7{50}\) rounded to three decimal places.

Consider \(\log_7{50}\)

Using property of logarithms,

\(\log_a b=\frac{\log_eb}{\log_ea}\)

Then given expression \(\log_7{50}\) becomes

\(\log_7 (50)=\frac{\log_e(50)}{\log_e7}\)

Also, \(\log_e50=3.91202...\\\log_e7=1.94591...\)

Substitute, we get,

\(\log_7 (50)=\frac{3.91202..}{1.94591...}\)

\(\log_7 (50)=2.010\)(rounded off 3 decimal place)

Thus, option (a) is correct.

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