Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. assume all variables are positive. log4x^2y , show work. i'll mark the brainliest!

If you meant "log to the base 10," then you have log 4*x^2*y, and this is equivalent to log 4 + 2log x + log y.

If you meant "log to the base 4," then you have:

log      x^2*y  =  log   x^2  +  log      y

      4                       4                   4    

and that simplifies to:              

log      x^2*y  =  2*log   x  +  log      y

      4                           4               4    

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions