find the values of the following,v)log a√a
Answers
We know the Logarithmic rules :
1 ) log a ( base a ) = 1
2 ) log ( a^m ) ( base a^n ) = m/n
3 ) log a^n = n log a
4 ) log 1 any base = 0
and
a^-n = 1/aⁿ
i ) log 5( base 25 )
= log 5¹ ( base 5² )
= 1/2
ii ) log 3 ( base 81 )
= log 3¹ ( base 3⁴ )
= 1/4
iii ) log ( 1/16 ) ( base 2 )
= log ( 1/2⁴ )( base 2 )
= log 2^-4 ( base 2 )
= -4 [ log 2 ( base 2 ) ]
= -4
iv ) log 1 ( base 7 )
= 0
v ) log √x ( base x )
= log x½ ( base x )
= 1/2 [ log x ( base x )]
= 1/2
vi ) log 512 ( base 2 )
= log 2^9 ( base 2 )
= 9 [ log 2 ( base 2 )]
= 9
vii ) log ( 0.01 )( base 10 )
= log ( 1/10 )² ( base 10 )
= log ( 10 )^-2 ( base 10 )
= -2 [ log 10 ( base 10 ) ]
= -2
viii ) log ( 8/27 ) ( base 2/3 )
= log ( 2/3 )³ ( base 2/3 )
= 3[ log (2/3 ) ( base 2/3 )]
= 3
I hope this helps you.
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Answer:
(i) log
3
(3
−4
)=−4log
3
3=−4
(ii) log
7
7
3
=3log
7
7=3
(iii) log
6
6
5
=5log
6
6=5
(iv) log
1/2
8=log
2
−1
2
3
=
−1
3
log
2
2=−3
(v) log
10
10
−4
=−4log
10
10=−4
(vi) log
3
9
3
=log
3
(
3
)
3
=5log
3
3
=5