Question

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

2.010



1.772



0.854



0.497

Answer 1

Hello there.

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

1.772

Answer 2

option (a) is correct.

`\log_7 (50)=2.010`

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=(\log_eb)/(\log_ea)`

Then given expression
`\log_7{50}` becomes

`\log_7 (50)=(\log_e(50))/(\log_e7)`

Also,
`\log_e50=3.91202...\\\log_e7=1.94591...`

Substitute, we get,

`\log_7 (50)=(3.91202..)/(1.94591...)`

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

Thus, option (a) is correct.