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प्रश्न
Solve : `[3^x]^2` : 3x = 9 : 1
उत्तर
`[3^x]^2` : 3x = 9 : 1
⇒ `[3^x]^2/3^x = 9/1`
⇒ `[3^x]^2 = 9 xx 3^x`
⇒ `[3^x]^2 = 3^2 xx 3^x`
⇒ `[3^x]^2 = 3^(x + 2)`
We know that if bases are equal, the powers are equal.
⇒ x2 = x + 2
⇒ x2 - x - 2 = 0
⇒ x2 - (2 - 1) x - 2 = 0
⇒ x2 - 2x + x - 2 = 0
⇒ x( x - 2 ) + 1( x - 2 ) = 0
⇒ ( x + 1 )( x - 2 ) = 0
⇒ x + 1 = 0 or x - 2 = 0
⇒ x = - 1 or x = 2.
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