Logarithmic equations help

Question

solve 

1)log₂4+2log₂8=x

 

2)log₅(x+2)-log₅ 7 = 2log₅3

 

thanks this site helps a lot!

Answer 1

1. Log₂4 + 2Log₂8 = X

 

Log₂2² + 2Log₂2³ = X

 

2Log₂2 +2*3Log₂2 = X

 

X=2*1 + 2*3

 

X = 2 +6

 

X =8

 

 

 

2. Log₅(X+2) -Log₅7 =2 Log₅3

 

Log₅((X+2)/7) = 2Log₅3

 

Log₅((X+2)/7) = Log₅3²

 

(x+2)/7 = 3²

 

X+2 = 7*9

 

X = 63 -2

 

X =61

 

 

 

 

Answer 2

(1)

 

     Log₂2² + Log₂2³ = x

 

     2 Log₂2 + 3 Log₂2 = x

 

     2•1 + 3•1 = x

     

     2 + 3 = x

     

     5 = x

 

(2)

 

     Log₅ ((x + 2)/7) = log₅ 3²

 

             (x + 2)/7 = 3²

 

             x + 2 = 7 • 9

 

             x = 63 - 2

 

             x = 61