Find the value of:7 1 + 3 2 + 4 3 - 2 6

Correct Answer is : log⁡18 18log18

Correct Answer is : log⁡18 18log18

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Logarithms Practice Test 1

Question : 19 of 40

Marks: +1, -0

7\log 1 + 3\log 2 + 4\log 3 - 2\log 6

Solution: 👈: Video Solution

Concept:

The logarithm laws convert coefficients into powers and combine sums/differences into products/quotients.

Explanation:

Use

a\log b = \log b^a

for each term.

7\log 1 + 3\log 2 + 4\log 3 - 2\log 6

= \log 1^7 + \log 2^3 + \log 3^4 - \log 6^2

= \log 1 + \log 8 + \log 81 - \log 36

Since

\log 1 = 0

, combine using

\log A + \log B - \log C = \log\left(\frac{AB}{C}\right)

= \log\left(\frac{8 \times 81}{36}\right)

= \log\left(\frac{648}{36}\right)

= \log 18

Answer:

The value is

\log 18

, so the correct option is B.

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