Question

How do you solve `Log( 4x - 3) = 2`?

Answer 1

`color(green)(x=103/4)`

Explanation:

It is important to remember the basic relation:

`color(red)("~~~~~~~~~~~~~~~~~~~~~~~~~~~")`
`color(red)("| ")color(blue)(log_b a =c)" means "color(blue)(b^c=a)color(red)(" |")`
`color(red)("~~~~~~~~~~~~~~~~~~~~~~~~~~~")`

(also remember that the default base for `log` is `10`)

Therefore
`color(white)("XXX")log(4x-3)=2 hArr log_10 (4x-3)=2`
means
`color(white)("XXX")10^2=4x-3`

`rarr 4x-3=100`

`rarr 4x=103`

`rarr x=103/4`