Using change of base (let new base be 2),the given problem can be written as
10log(x)/log(4x) + 21log(x)/log(16x) = 6log(x)/log(x/2)
Cancel log(x) from both side. You get
10/log(4x) + 21/log(16x) = 6/log(x/2)
10/[2 + log(x)] + 21/[4 + log(x) 6/[log(x) - 1]
Let log x to the base 2 is a, then
10/(2+a) + 21/(4+a) = 6/(a-1)
Simplify this equation and solve for a. From that find x.
Hello, alternative!
Use the Base-Change formula and change everything to base-2 . . .
. . . . . .
. .
. . . . . .
Factor: .
Multiply through by the LCD. . I'll drop the "base-2" for now.
. .
. . . . . . .
. . . . . .
And we have three equations to solve:
. .
. .
. .