If (under root 3/5) x+1 = 125/27 , find the value of x.
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(√3/5)ˣ⁺¹=125/27
or, (√3/5)ˣ⁺¹=(5/3)³
Taking log both sides,
(x+1)log√3/5=3log(5/3)
or, (x+1)(log√3-log5)=3log5-3log3
or, x+1=(3log5-3log3)/{log(3)¹/²-log5}
or, x={(3log5-3log3)/(1/2log3-log5)}-1
or, x=(3log5-3log3-1/2log3+log5)/(1/2log3-log5)
or, x=(4log5-7/2log3)/(1/2log3-log5)
or, x={(8log5-7log3)/2}/{(log3-2log5)/2}
or, x=(8log5-7log3)/(log3-2log5)
or, (√3/5)ˣ⁺¹=(5/3)³
Taking log both sides,
(x+1)log√3/5=3log(5/3)
or, (x+1)(log√3-log5)=3log5-3log3
or, x+1=(3log5-3log3)/{log(3)¹/²-log5}
or, x={(3log5-3log3)/(1/2log3-log5)}-1
or, x=(3log5-3log3-1/2log3+log5)/(1/2log3-log5)
or, x=(4log5-7/2log3)/(1/2log3-log5)
or, x={(8log5-7log3)/2}/{(log3-2log5)/2}
or, x=(8log5-7log3)/(log3-2log5)
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