Question

How do you solve `Log(3x–5)=3`?

Answer 1

`x=331 2/3`

Explanation:

Two very important things to remember when working with `log` function

1. `log(a)` means `log_(10) a`
   (The default base for the `log` function is `10`).

2. `color(black)(log_b a = c)` means `color(black)(b^c=a)`
   (Of the two this is the one you really need to memorize and practice using).

Applying this to the given example:
`log(3x-5)=3`

means
`color(white)("XXX")log_10(3x-5)=3`

which in turn means
`color(white)("XXX")10^3 = 3x-5`

We can simplify this as
`color(white)("XXXXX")1000 = 3x-5`

`rarrcolor(white)("XXX")995 = 3x`

`rarrcolor(white)("XXX")x=331 2/3`

Again, let me emphasize:
the general equivalence
`color(white)("XXX")color(red)(log_b a =c <=> b^c=a)`
is something most people do not grasp intuitively and should be memorized and worked with until it comes naturally.