Question

option.
What is the value of log 375 + 2log 15 -3 log 137
Given that, log 2 = 0.3012, log 3
= 0.4771 and log 5=0.6989​

Answer 1

Step-by-step explanation:

this is the answer for your question

Answer 2

The value of log 375 + 2log15 - 3log137 is -1.4843.

Given,

log 2 = 0.3012, log 3 = 0.4771, and log 5 = 0.6989

To find,

The value of log 375 + 2 log 15 - 3 log 137

Solution,

We can simply solve this numerical by following this process.

375 can be written as 125 x 3.

We get log 375 = log (125 x 3).

By the property of logarithm, log (a x b) = log a + log b. Hence, we get log 375 = log 125 + log 3.

Also, 125 can be written as 5^3. So, we get log 125 = log (5^3). By the property of logarithm, log(a^b) = b x log(a). Hence, we get log 125 = 3 log5

Here, we get log 375 = 3 log 5 + log 3. (equation 1)

2log15 = 2 log(5 x 3). Or, 2 log 15 = 2(log 5 + log 3).

Or, 2 log 15 = 2 log 5 + 2 log 3. (equation 2)

3 log 137 = 3 x 2.1367 (We find value of log 137 from log table). (Equation 3)

So, the final result will be equation1 + equation 2 - equation 3.

Or, (3 x 0.6989 + 0.4771) + (2 x 0.6989 + 2 x 0.4771) - (3 x 2.1367)

(Put values of log 2, log 3, and log 5 above)

So, we get 2.5738 + 2.352 - 6.4101 = -1.4843.

This is the final answer. The value of log 375 + 2log15 - 3 log 137 = -1.4843.

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