Question

Log5x-log4=2 solve the equation

Answer 1

x = 80

Explanation:

using the rules of logarithms

log x - log y = log (
`(x)/(y)` )

`log_(b)` x = n ⇒ x =
`b^(n)`

given

log5x - log4 = 2

log (
`(5x)/(4)` ) = 2

note that log is actually
`log_(10)`

then

`log_(10)` (
`(5x)/(4)` ) = 2

`(5x)/(4)` = 10² = 100 ( multiply both sides by 4 to clear the fraction )

5x = 400 ( divide both sides by 5 )

x = 80