Logarithms Practice Test 1

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Question : 37 of 40

Marks: +1, -0

If

{\log x}/{\log 5}={\log 36}/{\log 6}={\log 64}/{\log y}

what are the values of

x

and

y

respectively?

8, 25
25, 8
8, 8
25, 25

Solution:

{\log x}/{\log 5}={\log 36}/{\log 6}={\log 64}/{\log y}

Since,

{\log x}/{\log 5}={\log 36}/{\log 6}

⇒{\log x}/{\log 5}={\log 6^2}/{\log 6}

⇒{\log x}/{\log 5}={2\log 6 }/{\log 6}

⇒\log x=2 \log 5

∴x^2=5^2=25

Again,

{\log 64}/{\log y}={\log 36}/{\log 6}

⇒{\log 2^6}/{\log y}={\log 6^2}/{\log 6}

⇒{6\log 2 }/{\log y}={2\log 6 }/{\log 6}

⇒\log y=3\log 2

⇒y=2^3=8

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