Help Please...3 Problems that are logarithmic??

I don't quite understand the first one, Phoenix....are we multiplying log(5) by 125???

2.  

5 * 8^(4x) = 376          divide both sides by 5

8^(4x) =  376 / 5        take the log of both sides

log 8^(4x) = log (376 / 5)       

Remember   that      log a^b    can be written as   b*log (a)

So

(4x) log (8)  = log (376/5)

x *(4 * log 8)   =  log (376 / 5)        divide both sides by  (4 * log 8)

x =   log (376/5) / [ 4 * log 8 ]    =  log (75.2) / (4log 8)

Last one

The key here is to notice that  81  =  3^4

The reason for doing this is that we won't have to use any logs to solve for x

So....we actually have

3^(7x)  =  (3^4)^(x + 9)

Remember that    (a^m)^n  =  a^(m * n)       so.....

3^(7x) =  3^(4 * (x + 9) )

Since the bases are the same, we can solve for the exponents

7x  =  4 (x + 9)     simplify

7x  = 4x + 36      subtract 4x from both sides

3x = 36    divide both sides by 3

x = 12