Question

8=5+2log(x/4) solve for x

Answer 1

8 = 5 + 2log(x/4)

First, I like to put the log on the left side, so switch the sides.

5 + 2log(x/4) = 8

Subtract 5 from each side

2log(x/4) = 3

Divide both sides by 2

log(x/4) = 3/2

When using logs, one of the rules is that x = logy(y^x). Apply this. Use 10 for y because by default log uses 10. Use 3/2 for x.

3/2 = log10(10^3/2) = log10(10$\sqrt{10}$)

Now we have log10(x/4) = log10(10$\sqrt{10}$)

Both have the same log base, so eliminate the logs.

x/4 = 10$\sqrt{10}$

Multiply everything by 4 to get x by itself

x = 40$\sqrt{10}$