Solve for x (logarithmic question)

Question

(log₅ 2x)³ - log₅ (2x)³ = 0

Answer 1

let log₅2x = y

y^3 = 3y

y^2 = 3

y = +sqr3

log₅2x =y

rewrite in exponential form

2x = 5^y = 5^(+sqr3) = about 16.24 or 1/16.24

x = 16.24/2 = about 8.12 or 1/32.48 =.03

x = 8.12 or 0.03

Answer 2

(log₅ 2x)³ - log₅ (2x)³ = 0

and so [log₅(2x)]³=3log₅(2x)

correction: when dividing out log₅(2x) need to account for log₅(2x)=0 (since 0=0 is valid) gives third answer of x=1/2

log₅(2x)=(+/-)√3

2x=5^(+/-)√3

x=half of 2x