Each logarithm should involve only one variable and should not have any exponents. Assume that all variables are positive. log(zy^3)=?

Adrian Brown

Adrian Brown

Answered question

2022-11-08

Each logarithm should involve only one variable and should not have any exponents. Assume that all variables are positive.
log ( z y 3 ) = ?

Answer & Explanation

sliceu4i

sliceu4i

Beginner2022-11-09Added 16 answers

It is given that, log ( z y 3 )
To expand log ( z y 3 ) using the properties of logarithms.
As, log ( A B ) = log ( A ) + log ( B ) by the basic definition of logarithms
log ( z y 3 ) can be written as log ( z ) + log ( y ) 3
i.e. log ( z y 3 ) = log ( z ) + log ( y ) 3 log ( z y 3 ) = log ( z ) + 3 log ( y )  using  log ( m ) n = n log ( m )
Hence, the required expansion of log ( z y 3 ) is equal to log ( z ) + 3 log ( y )

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