Using laws of logarithms, write the expression below as a single logarithm. 5log(16-x^2)-(log(4+x)+log(4-x))

Hanna Webster

Hanna Webster

Answered question

2022-11-07

Using laws of logarithms, write the expression below as a single logarithm.
5 log ( 16 x 2 ) ( log ( 4 + x ) + log ( 4 x ) )

Answer & Explanation

sliceu4i

sliceu4i

Beginner2022-11-08Added 16 answers

we will use the following exponential rules :
log   a b = log   a + log   b log   a b = log   a log   b
We have given,
5   log ( 16 x 2 ) ( log ( 4 + x ) + log ( 4 x ) ) 5   log ( 4 2 x 2 ) ( log ( 4 + x ) + log ( 4 x ) ) 5   log ( 4 + x ) ( 4 x ) log ( 4 + x ) log ( 4 x ) 5   [ log ( 4 + x ) + log ( 4 x ) ] log ( 4 + x ) log ( 4 x ) 5 log ( 4 + x ) + 5 log ( 4 x ) log ( 4 + x ) l o g ( 4 x ) 4 log ( 4 + x ) + 4 log ( 4 x ) 4   [ log ( 4 + x ) + log ( 4 x ) ] 4   [ log ( 4 + x ) ( 4 x ) ] 4 log ( 16 + x 2 ) log ( 16 + x 2 ) 4
Answer: log ( 16 + x 2 ) 4

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