Find the value of _{c³ a³ b³.

Correct Answer is : log⁡a+log⁡blog⁡c a+ b/ clogcloga+logb

Correct Answer is : log⁡a+log⁡blog⁡c a+ b/ clogcloga+logb

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Logarithms Practice Test 1

Question : 7 of 40

Marks: +1, -0

\log_{c^3} a^3 b^3

Solution: 👈: Video Solution

Concept:

Use the change-of-base formula to simplify a logarithm whose base and arguments are powers.

Explanation:

Let the given expression be

\log_{c^3}(a^3 b^3)

Apply the change-of-base formula:

\log_{c^3}(a^3 b^3)=\frac{\log(a^3 b^3)}{\log(c^3)}

Expand the numerator using

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

\frac{\log(a^3 b^3)}{\log(c^3)}=\frac{\log a^3+\log b^3}{\log c^3}

Use the power rule

\log x^n=n\log x

=\frac{3\log a+3\log b}{3\log c}

Cancel the common factor

3

=\frac{\log a+\log b}{\log c}

Answer:

The required value is

\frac{\log a+\log b}{\log c}

So the correct option is B.

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