given that log5(y)=8 find the value of log5(125y)?

log₅(125y)
= log₅(125) + log₅(y)
= log₅(5³) + 8
= 3 log₅(5) + 8
= 3 + 8
= 11

log(base 5)(125y) =
log(base 5)125 + log(base 5)y =
3 + 8 =
11

Log[5](y) = 8 → recall: Log[a](x) = Ln(x) / Ln(a) ← where a is the base

Ln(y) / Ln(5) = 8

Ln(y) = 8.Ln(5)



= Log[5](125y)

= Ln(125y) / Ln(5)

= [Ln(125) + Ln(y)] / Ln(5)

= [Ln(5³) + Ln(y)] / Ln(5)

= [3.Ln(5) + Ln(y)] / Ln(5) → recall: Ln(y) = 8.Ln(5)

= [3.Ln(5) + 8.Ln(5)] / Ln(5)

= [11.Ln(5)] / Ln(5)

= 11