How do I solve $log_sqrt5$ $0.2$ ?

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Answer 1 · 2017-10-14T07:35:56

$-2.$

We know that, $log_a y=x iff a^x=y.$

$"So, if, "log_sqrt5 0.2=x," then, "(sqrt5)^x=0.2.$

$:. (5^(1/2))^x=0.2=2/10=1/5.$

$:. 5^(x/2)=5^(-1).$

$:. x/2=-1.$

$:. x=-2.$

$rArr log_sqrt5 0.2=-2.$

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