If \log_a (19^3/{\sqrt^4 3^5\times7^2})=3\log_a19-2\log_a 7-x then which one of the following is true?

Logarithms Practice Test 2

Question : 2 of 39

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\log_a (19^3/{√^4 3^5×7^2})=3\log_a19-2\log_a 7-x

then which one of the following is true?

Solution:

\log_a (19^3/{√^4 3^5×7^2})=3\log_a19-2\log_a 7-x

⇒\log_a19^3-\log_a(√^4 3^5×7^2)=3\log_a19-2\log_a 7-x

⇒3\log_a19 -\log_a 3^{5/4} -2\log_a7 =3\log_a19-2\log_a 7-x

⇒\log_a 3^{5/4}=x

⇒a^x=3^{5/4}

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