Find the value of log✓15+log2-log6-½

Answer 1

that would be
1/2 log15 + log2 + 1/2 log6
log √(15*4*6) = log√360 = 1/2 log360 = ____

Answer 2

If log means log₁₀ ( logarithm for base 10 ) then:

log ( √10 ) = 1 / 2 log ( 10 ) = 1 / 2 ∙ 1 = 1 / 2

1 / 2 = log ( √10 )

log ( √15 ) + log ( 2 ) - log ( 6 ) - 1 / 2 =

log ( √15 ) + log ( 2 ) - log ( 6 ) - log ( √10 ) =

1 / 2 log ( 15 ) + log ( 2 ) - log ( 6 ) - 1 / 2 log ( 10 ) =

1 / 2 log ( 3 ∙ 5 ) + log ( 2 ) - log ( 2 ∙ 3 ) - 1 / 2 log ( 2 ∙ 5 ) =

1 / 2 [ log ( 3 ) + log ( 5 ) ] + log ( 2 ) - [ log ( 2 ) + log ( 3 ) ] - 1 / 2 [ log ( 2 ) + log ( 5 ) ] =

1 / 2 log ( 3 ) + 1 / 2 log ( 5 ) + log ( 2 ) - log ( 2 ) - log ( 3 ) - 1 / 2 log ( 2 ) - 1 / 2 log ( 5 ) =

1 / 2 log ( 3 ) + 1 / 2 log ( 5 ) - log ( 3 ) - 1 / 2 log ( 2 ) - 1 / 2 log ( 5 ) =

1 / 2 log ( 3 ) - log ( 3 ) + 1 / 2 log ( 5 ) - 1 / 2 log ( 5 ) - 1 / 2 log ( 2 ) =

- 1 / 2 log ( 3 ) - 1 / 2 log ( 2 ) =

- 1 / 2 [ log ( 3 ) + log ( 2 ) ] =

- 1 / 2 log ( 3 ∙ 2 ) =

- 1 / 2 log ( 6 ) = log ( 1 / √ 6 )