CAT Exam Model Paper 2 with solutions for free online practice

Question : 91 of 100

Marks: +1, -0

What are the roots of the equation

2 ^ { x + 2 } , 27 ^ { { x } /{ x - 1 } } = 9 ?

Solution:

2 ^ { x + 2 } , 27 ^ { { x } /{ x - 1 } } = 9

On taking log both sides, we get

( x + 2 ) \log 2 + { x }/ { x - 1 } \log 27 = \log 9

⇒( x + 2 ) \log 2 + { 3 x } /{ x - 1 } \log 3 = 2 \log 3

⇒( x + 2 ) \log 2 + ( { 3 x }/ { x - 1 } - 2 ) \log 3 = 0

⇒( x + 2 ) \log 2 + ( { x + 2 }/ { x - 1 } ) \log 3 = 0

⇒( x + 2 ) [ \log 2 + { 1 }/ { x - 1 } \log 3 ] = 0

⇒x + 2 = 0

\log 2 + { 1 }/ { x - 1 } \log 3 = 0

⇒x = - 2

( x - 1 ) = - { \log 3 }/ { \log 2 }

∴x = - 2

x = 1 - ( { \log 3 }/ { \log 2 } )

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