Solve -log base 8 (2) + 5 log base 8 (2) + (1/2) log base 8 (16)

easternerjx

easternerjx

Answered question

2022-09-23

Solve
log 8 2 + 5 log 8 2 + 1 2 log 8 ( 16 )

Answer & Explanation

maceratorti

maceratorti

Beginner2022-09-24Added 10 answers

Step 1
Given
log 8 2 + 5 log 8 2 + 1 2 log 8 ( 16 )
= log 8 ( 2 ) + log 8 ( 2 ) 5 + log 8 ( 16 ) 1 2
= log 8 2 + log 8 32 + log 8 ( 4 )
We know
log a log b = log ( a b ) ; x log a = log a x
log a + log b = log ( a b )
log 8 2 + log 8 ( 32 × 4 )
Step 2
log 8 ( 32 × 4 2 ) = log 8 ( 64 )
= log 8 ( 8 ) 2 = 2 log 8 ( 8 ) = 2
[ log 8 8 = 1 ]
Hence,
log 8 ( 2 ) + 5 log 8 ( 2 ) + 1 2 log 8 ( 16 ) = 2

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