Question

5 log3+7log2-3log11-4log5 solve this​

Answer 1

Step-by-step explanation:

5 log3+7log2-3log11-4log5

= log3⁵ + log2⁷ - log11³ - log5⁴

= log(243×128÷1331÷625)

= log0.0374

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Answer 2

Final Answer:

The simplified result of the logarithmic expression $5 log3+7log2-3log11-4log5$ is 0.03739.

Given:

The logarithmic expression $5 log3+7log2-3log11-4log5$ is provided.

To Find:

The value of the logarithmic expression $5 log3+7log2-3log11-4log5$ is is to be calculated.

Explanation:

The  logarithmic formulae that are important to lead to the solution to the present problem are as follows

1. $logM+logN =log(MN)$
2. $logM-logN =log(\frac{M}{N})$
3. $alogM =log(M^a)$

Step 1 of 3

Simplify the logarithmic expression given in the problem using the above formula 3 in the following way.

$5 log3+7log2-3log11-4log5\\=log3^5+log2^7-log11^3-log5^4$

Step 2 of 3

Using the above formulae 1 and 2, simplify the above expression further in the following way.

$=log3^5+log2^7-log11^3-log5^4\\=log(\frac{3^5\times 2^7 }{11^3 \times 5^4} )$

Step 3 of 3

In continuation with the above calculations, the simplified form of the stated logarithmic expression is

$log(\frac{3^5\times 2^7 }{11^3 \times 5^4} )\\=log(\frac{31104}{831875)} \\=0.03739$

Therefore, the required correct answer is 0.03739.

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