Find the value of: 5 2 + 2 5 + 3 1

Correct Answer is : log⁡800 800log800

Correct Answer is : log⁡800 800log800

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Logarithms Practice Test 2

Question : 20 of 39

Marks: +1, -0

5 \log 2 + 2 \log 5 + 3 \log 1

Solution:

Concept:

Use the log laws:

a\log b = \log b^a

and

\log x + \log y = \log(xy)

Explanation:

Given:

5\log 2 + 2\log 5 + 3\log 1

Apply the power rule:

5\log 2 = \log 2^5 = \log 32

2\log 5 = \log 5^2 = \log 25

3\log 1 = \log 1^3 = \log 1 = 0

So, the expression becomes

\log 32 + \log 25 + \log 1

Use the product rule:

\log(32 \times 25 \times 1)

Since

32 \times 25 = 800

, the value is

\log 800

Answer:

\log 800

, which is option C.

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