(EMERGENCY)Logarithms (Simultanoius equation)

Question

Given that a and b are positive constants. Find a and b 

 

ab=25

Log₄a - log₄b =3

Answer 1

Focusing on the second equation, you can combine the left side using the property of subtracting logarithms with the same base.  Once you do this, you should be able to determine what (a/b) is equal to, using the definition of the logarithm function.  The first equation tells you what (a*b) is equal to already, so the remainder of the problem is simple algebra.

Answer 2

ab=25

log₄a-log₄b=3

log₄(a/b)=3

4³=a/b

64=a/b

64b=a

ab=25

(64b)(b)=25

64b²=25

b²=25/64

take the square root of both sides

b=5/8

ab=25

(5/8)a=25

(8/5)(5/8)a=(8/5)25

a=40

a=40 and b=5/8