# What is x if #log_4(8x ) - 2 = log_4 (x-1)#?

##### 1 Answer

Nov 1, 2015

#### Explanation:

We would like to have an expression like

- First of all, note that
#4^2=16# , so#2=log_4(16)# .

The equation then rewrites as

But we're still not happy, because we have the difference of two logarithms in the left member, and we want a unique one. So we use

#log(a)-log(b)=log(a/b)#

So, the equation becomes

Which is of course

Now we are in the desired form: since the logarithm is injective, if

Which is easily solve into