Question

Determine the value of the following.
(i) log₂₅5 (ii) log₈₁3 (iii) log₂(1/16)
(iv) log₇1 (v) logₓ√x (vi) log₂512
(vii) log₁₀0.01 (viii) log₍₂/₃)(8/27)

Answer 1

In the attachments I have answered this problem.   I have listed the formulae which I applied in the given problems.  I hope this answer helps you   See the attachment for detailed solution.  

Answer 2

Hi ,

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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

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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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