If 2=a, 3=b, 7=c and 6^{x}=7^{x+4}, then x=

Correct Answer is : 4ca+b−c\;4c/a+b-ca+b−c4c

Correct Answer is : 4ca+b−c\;4c/a+b-ca+b−c4c

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Logarithms

Question : 56 of 85

Marks: +1, -0

\log 2=a, \log 3=b, \log 7=c

6^{x}=7^{x+4}

x=

Solution:

Concept:

Take logarithms of both sides to solve for

x

in terms of given logs.

Explanation:

Start with

6^{x} = 7^{x+4}

Take log (common) on both sides:

x \log 6 = (x+4) \log 7

Expand:

x \log 6 = x \log 7 + 4 \log 7

Bring

x

terms together:

x \log 6 - x \log 7 = 4 \log 7

Factor

x

x (\log 6 - \log 7) = 4 \log 7

Thus

x = \frac{4 \log 7}{\log 6 - \log 7}

Now

\log 6 = \log(2 \times 3) = \log 2 + \log 3 = a + b

, and

\log 7 = c

Substitute:

x = \frac{4c}{(a+b) - c} = \frac{4c}{a+b-c}

Answer:

x = \frac{4c}{a+b-c}

, which matches option B.

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