Question 744922
Given log(base 3)10= 2.0959 find an approximation for each logarithm
{{{log(3,(10))=2.0959}}}
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a) log(base 3)1000
{{{log(3,(1000))=log(3,(10^2))=2log(3,(10))=2*2.0959=4.1918}}}
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b) log(base 3)30
{{{log(3,(30))=log(3,(3*10))=log(3,(3))+log(3,(10))=1+2.0959=3.0959}}}
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c) log(base 3)√0.3
{{{log(3,sqrt(0.3))
=(1/2)log(3,(0.3))
=(1/2)log(3,(3/10))
=(1/2)log(3,(3))-log(3,(10))=(1/2)(1-2.0959)=-0.5479}}}
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d) log(base 3)(100/9)
{{{log(3,(10^2/3^2))
=log(3,(10^2))-log(3,(3^2))
=2log(3,(10))-2log(3,(3))=2*2.0959-2*1=2.1918}}}