(2log(a)x)/(log(b)3)-(log(b)27)/(log(a)x)=5?

Question

How would you solve this if b=a^2

Answer 1

if b=a^2, then you can substitute 1/2 for log(a)/log(b)

Answer 2

2log(a)x)/(log(b)3) - (log(b)27/log(a)x = 5
if b = a^2,
2log(a)x)/(log(a^2)3) - (log(a^2)27/log(a)x = 5
2log(a)x)/(2log(a)3) - (2log(a)27/log(a)x = 5
x/3 - 54/x = 5
x^2 - 162 = 15x
x^2 - 15x - 162 = 0
162 = 2*3*3*3
(x + 3)(x - 18) = 0
x = -3, 18