Can I please get some help on these three?????

Question

3 log 4 - log 3 =
 

log (4/3)^3

log 4

log (7/3)

log 64 / log 3

log (64/3)
 

 

 

 

log 2(x^3)(y^-2) =
 

log 2 + 3 log x - log 1/y^2

6 log x - 2 log y

log 2 + log 3x - 2 log y

log 2 + 3 log x / 2 log y

log 2 + 3 log x - 2 log y
 

 

 

 

log 63 – log 9 =
 

log 54

(log 63) / (log 9)

log 7

log 567

9 log 7

Answer 1

3 log 4 - log 3 = log 4³ - log 3 = log (4³/3) = log 64/3

 

log 2x³y^-2 = log 2 + log x³ + log y^-2 = log 2 + 3 log x - 2log y

 

log 63 - log 9 = log 63/9 = log 7

Answer 2

1)  3 log 4 - log 3 =

 

Note a(log b) = log b^a so 3 log 4 = log 4³ 

 

log 4³ - log 3 = log 64 - log 3

 

Note: log a - log b = log a/b

 

log 64 - log 3 = log(64/3)

 

2)  log 2(x^3)(y^-2) =

 

     = log [(2x³)(y^-2)]

Note:  log (ab) = log a + log b

     = log(2x³) + log(y^-2)

    = log 2 + log x³ -2log y

    = log 2 + 3log x -2 log y

 

3)  log 63 – log 9 =

     log (63/9) =

     log 7