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Question
Find x, if : `( sqrt(3/5))^( x + 1) = 125/27`
Solution
`( sqrt(3/5))^( x + 1) = 125/27`
⇒ `[(3/5)^(1/2)]^( x + 1 ) = [ 5 xx 5 xx 5 ]/[ 3 xx 3 xx 3]`
⇒ `(3/5)^[( x + 1 )/2] = (5/3)^3`
⇒ `(3/5)^[( x + 1 )/2] = (3/5)^- 3`
We know that if bases are equal, the powers are equal
⇒ `[ x + 1 ]/2 = -3`
⇒ x + 1 = - 6
⇒ x = - 6 - 1
⇒ x = - 7
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