Question

3. Solve 2log4y - log4 (5y - 12) = 1/2​

Answer 1

Answer:

y =  4  or y = 6

Step-by-step explanation:

2log4y - log4 (5y - 12) = 1/2

​2log_4(y) - log_4(5y-12) = log_4(2)           apply law of logarithms

log_4(y^2) + log_4(1/(5y-12)) = log_4(/2)    apply law of logarithms

log_4(y^2/(5y-12)) = log_4(2)                     remove logarithm

y^2/(5y-12) = 2                                            cross multiply

y^2 = 10y-24                                                  rearrange and factor

y^2 - 10y + 24 = 0

(y-4)(y-6) = 0

y= 4 or y=6