Condensing Fractional Logarithms Does the following condense to the following: log_2 z+(log_2 x)/2+(log_2 y)/2=log_2 (zsqrt(x) sqrt(y)) or to log_2(z sqrt(xy)) ?

brasocas6 2022-08-11 Answered
Condensing Fractional Logarithms
Does the following condense to the following:
log 2 z + ( log 2 x ) / 2 + ( log 2 y ) / 2 = log 2 ( z x y ) or to log 2 ( z x y )?
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Answers (2)

optativaspv
Answered 2022-08-12 Author has 14 answers
Both of your answers are correct!
log 2 z + log 2 x 2 + log 2 y 2 = log 2 z + log 2 x 1 2 + log 2 y 1 2 = log 2 ( z x y ) = log 2 ( z x y )
We used the identities:
log a + log b = log ( a b )
x log a = log a x
and
a b = a b
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opositor5t
Answered 2022-08-13 Author has 5 answers

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