Question

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) =

Answer 1

• 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

Answer 2

• -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