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100 points Given log34≈1.262 and log37≈1.771, what is the value of log3(7 / 16)? Use three decimal places log3(7 / 16) =
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14 votes
14 votes
100 points

Given log34≈1.262 and log37≈1.771, what is the value of log3(7 / 16)?
Use three decimal places
log3(7 / 16) =

100 points Given log34≈1.262 and log37≈1.771, what is the value of log3(7 / 16)? Use-example-1
User Riho
by
3.0k points

2 Answers

13 votes
13 votes
  • log(a/b)=loga-logb

So

  • log_3(7/16)
  • log_3(7)-log_3(16)
  • log_3(7)-log_3(4²)
  • log_3(7)-2log_3(4)
  • 1.771-2(1.262)
  • -0.753
User Nafi
by
2.7k points
12 votes
12 votes

Answer:

  • -0.753

Explanation:

Given

  • log₃4 ≈ 1.262 and
  • log₃7 ≈ 1.771

To find

  • log₃(7/16)

Solution

  • log₃(7/16) =
  • log₃7 - log₃16 =
  • log₃7 - 2log₃4 =
  • 1.771 - 2*1.262 =
  • -0.753

User Kalliopi
by
3.5k points
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