Question

If log 2=0.3010,log 3=0.4771,log 7=0.8450 find the value of log 84

Answer 1

Answer:

If log 2=0.3010,log 3=0.4771,log 7=0.8450 find the value of log 84 is 1.9241

Step-by-step explanation:

Let's first write 84 as a product of its prime factors below:

84 = 2 × 2 × 3 × 7

Writing it in form of log we have:

Log 84 = Log (2 × 2 × 3 × 7)

This equals to:

Log 84 = log 2 + log 2 + log 3 + log 7

Substituting the values we have:

log 84 = 0.3010 + 0.3010 + 0.4771 + 0.8450

Adding up we have:

log 84 = 1.9241

Answer 2

The value of log 84 is 1.9241

• Given,

               log 2 = 0.3010     ----------(1)

               log 3 = 0.4771      ----------(2)

               log 7 = 0.8450     ----------(3)

               log 84 = ?

• Factorizing 84, we get

              84 = 2 x 2 x 3 x 7

              84 = $2^{2}$ x 3 x 7

• Applying log on both sides

              log 84 = log ($2^{2}$ x 3 x 7)

                          = log $2^{2}$ + log 3 + log 7

                          = 2log 2 + log 3 + log 7

                          = 2(0.3010) + 0.4771 + 0.8450 [from (1), (2), (3)]

              log 84 = 1.9241