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solve for x: log1/3(x-1) + log1/3(x+1) + log√3(5-x) < 1 plz helpppp.....
solve for x:
log1/3(x-1) + log1/3(x+1) + log√3(5-x) < 1
plz helpppp.....
logax = logx/loga (property) logxb = blogx (property) log1/3(x-1) + log1/3(x+1) + log (5-x) < 1 logx-1/log1/3 + logx+1/log1/3 + log5-x/log√3 <1 -logx-1/log3 - logx+1/log3 + 2log5-x/log3 <1 -logx-1 - logx+1 + 2log5-x < log3 (logab = loga + logb) 2log5-x - logx2-1 < log3 2log5-x < log3 + logx2-1 2log5-x < log3(x2-1) (5-x)2 < 3(x2-1) now solve this & get the ans
logax = logx/loga (property)
logxb = blogx (property)
log1/3(x-1) + log1/3(x+1) + log (5-x) < 1 logx-1/log1/3 + logx+1/log1/3 + log5-x/log√3 <1 -logx-1/log3 - logx+1/log3 + 2log5-x/log3 <1 -logx-1 - logx+1 + 2log5-x < log3 (logab = loga + logb) 2log5-x - logx2-1 < log3 2log5-x < log3 + logx2-1 2log5-x < log3(x2-1) (5-x)2 < 3(x2-1) now solve this & get the ans
log1/3(x-1) + log1/3(x+1) + log (5-x) < 1
logx-1/log1/3 + logx+1/log1/3 + log5-x/log√3 <1
-logx-1/log3 - logx+1/log3 + 2log5-x/log3 <1
-logx-1 - logx+1 + 2log5-x < log3 (logab = loga + logb)
2log5-x - logx2-1 < log3
2log5-x < log3 + logx2-1
2log5-x < log3(x2-1)
(5-x)2 < 3(x2-1)
now solve this & get the ans
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