solve round to the 4th decimal place

Question

log_3(5x)- log₃₍₆₎₌₂

Answer 1

I will change first of all the base, reaching:

Log₃(5x) - Log₃(6) = 2; changing the base I get

(log₁₀(5x)/log₁₀(3)) - (log₁₀(6)/log₁₀(3)) = 2

Log₁₀(5x) - log₁₀(6) = 2 log₁₀(3)

log₁₀(5x) = 2 log₁₀(3) +log₁₀(6)

log₁₀(5x) = log₁₀(9) + log₁₀(6)

log₁₀(5x) = Log₁₀(9*6) = log₁₀(54)

5x = 54

x = 54/5 = 10.8000

 

Answer 2

log ₃(5X) - log₃(6) = 2

 

log₃(5x) / 6 = log₃ 3²

 

       5X/ 6 = 9

 

        X = 54/5 = 10 4/5