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

brasocas6

Answered question

2022-08-11

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 )?

Answer & Explanation

optativaspv

optativaspv

Beginner2022-08-12Added 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
opositor5t

opositor5t

Beginner2022-08-13Added 5 answers

Both are the same, since x y = x y

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