How do you solve 2ln (2x+5) = 8?

Well you have to use one of the logarithm laws

b * ln (x) = ln (x^b)

So

2 ln (2x + 5) = 8

ln [ (2x+5) ^2] = 8

So now if we do e^x on both sides and we say that x is going to be what either side equals like this

e^ (ln [ (2x+5) ^2]) = e^8

We we know that

e^[ln (x) ] = x so

[ (2x+5) ^2] = e^8

take square root of both sides

2x + 5 = e^4. and - (2x+5) = e^4

2x = e^4 - 5. and - 2x = e^4 + 5

x = (e^4 - 5) / 2 and x = (e^4 + 5) / - 2

now just use a calculator to solve