Question

How do you solve `log_(2x+1) N - log_4x = log_2 3`?

Answer 1

`x=1/2, N = 3 sqrt(2)/2`

Explanation:

`log_(2x+1) N - log_4x = log_2 3`

We know that

`log_4x =log_e x/(log_e 2^2)=1/2log_e x/(log_e 2) = 1/2 log_2 x`

so

`log_(2x+1) N= log_2 3+1/2log_2 x=log_2(3 sqrt(x))`

Now making equivalents of argument and basis

`{(N = 3 sqrt(x)), (2x+1=2):}`

Solving for `N, x` we get at

`x=1/2, N = 3 sqrt(2)/2` which is a solution.

Of course there are infinite solutions according to the attached figure in which appear the solution points for `N` vertical and `x` horizontal.