find the value of (10^{-5})^{1/2} using log

Let,

y=(10^{-5})^{1/2}

Taking log on both sides,

log y=log (10^{-5})^{1/2}

log y=1/2 log(10^{-5}) [We know log a^{y}=y log a]

log y=1/2 log(1/10^{5})

log y=1/2 [log1-log 10^{5}] [we know log(a/b)=log a-log b]

logy=1/2 [0-log10^{5}] [log1=0]

logy=1/2 [-log10^{5}]

logy=1/2 [-5 log10] [We know log a^{y}=y log a]

logy=-5/2 log10

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