Question 554033
if log(x^5y^3) = 25, this means that:
10^25 = x^5y^3
if log(x/y) = 3, this means that:
10^3 = x/y
we can solve for x in this equation to get:
x = 10^3y
we can substitute in the equation of:
10^25 = x^5y^3 to get:
10^25 = (10^3y)^5*y^3
this becomes:
10^25 = 10^15y^5*y^3
we simplify this to get:
10^25 = 10^15*y^8
we divide both sides of this equation by 10^15 to get:
10^25/10^15 =y^8
we simplify to get:
10^10 = y^8
we take the 8th root of both sides of this equation to get:
10^(10/8) = y which simplifies to:
10^(1.25 = y which leads to:
y = 17.78279410
since x = 10^3y which is the same as 1000y, this means that:
x = 17782.79410
y = 17.7829410
with those values for x and y, we get:
first equation:
log(x^5*y^3) = log(17782.79410^5*17.7829410^3) = log(10^25) = 25
second equation:
log(x/y) = log(17782.794/17.7829410) = log(1000) = 3
all the numbers check out.
the values for x and y are good.
x = 17782.79410
y = 17.7829410
log(x) = log(17782.79410) = 4.25
log(y) = log(17.7829410) = 1.25
your answer to the question is:
log(x) = 4.25