Question

log3=0.4771 then what is value of log3000.And explain about it

Answer 1

Concept

The exponent or power that must be applied to a base in order to get a particular number is logarithm

Given

log3=0.4771,

Find

We need to find the value of log3000

Solution

log3000,

log(3×1000),

log3+log1000, (since logmn=logm+logn),

0.04771 + log10³,

0.4771 + 3log10, (since logm^n = nlogm),

then it becomes,

0.4771 + 3×1, (since log10=1),

0.4771 + 3,

= 3.4771

Hence the value of log 3000 is 3.4771

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Answer 2

Answer:

The value of log3000 is 3.3771.

Step-by-step explanation:

Some rules of logarithm are,

• log $a$ + log $b$ = log ($ab$)
• log a - lob b = log$\left(\frac{a}{b} \right)$
• log 1 = 0
• log 10 = 1
• log $10^n$ = $n$

Step 1 of 1

It is given that the value of log3 = 0.4771.

To find the value of log3000.

Consider the logarithm function as follows:

log3000

Rewrite the function as follows:

⇒ log3000 = log (3×1000)

Using the rules of logarithm, we get

⇒ log3000 = log 3 + log1000

⇒ log3000 = log 3 + log$10^3$

⇒ log3000 = log 3 + 3 (log $10^n$ = $n$) . . . . . (1)

Now,

Substitute the value of log3 in the function (1) as follows:

⇒ log3000 = 0.4771 + 3

⇒ log3000 = 3.4771

Therefore, the value of log3000 is 3.3771.

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