How do I solve 6ln(x-4)=1

In words it is six times natural log of x minus four equals one.

6ln(x-4) = 1
We want to solve for x so we want to rearrange and move everything over to the other side.

Firstly, you have 6 TIMES ln(x-4)
Take that TIMES 6 to other side by DIVIDING 6. So we get:
ln(x-4) = 1/6

Now we have the ln to deal with. To get rid of ln, we have to do the inverse of it. To do that, we put e as a base and raise everything as a power/indice like this:
e^[ln(x-4)] = e^1/6
The e and the ln cancel each other so we get
x-4 = e^1/6

Now we take the MINUS 4 to the other side by ADDING 4. We get:
x = (e^1/6) + 4
x = 5.18 to 3 significant figures.

6 * ln(x - 4) = 1=> divide by 6 both sides
ln(x - 4) = 1/6 => Put both sides to the power of e Note e^Log(y) reduces to just y
x - 4 = e ^ (1/6) => add 4 to both sides
x = (e ^ (1/6)) + 4 => this is the solution

ln(x-4) = 1/6
x-4 = e^(1/6)
x = e^(1/6) + 4

Damn my sister borrowed my calculator so I can't calculate x. Hope this helps!

The equation can be written

ln(x-4) = 1/6

Hence x-4 = e^(1/6)

x = 4 + e^(1/6)

ln(x-4) = 1/6
x-4 = e^(1/6)
x = 4 + e^(1/6) = 5.18136041286564598030511215250718432783…

ln(x-4) = 1/6

x-4 = e^(1/6)
x= e^(1/6) + 4

6 * ln(x - 4) = 1
ln(x - 4) = 1/6
x - 4 = e ^ (1/6)
x = (e ^ (1/6)) + 4