# Math Help - Logarithmic equations

1. ## Logarithmic equations

Can i get some help with this equation please??

Solve the logarithmic equation:

2. HINT:
$log_5 (5 - 4x) = \frac{{\ln (5 - 4x)}}{{\ln (5)}}\;\& \,\log _{\sqrt 5 } (2 - x) = \frac{{2\ln (2 - x)}}{{\ln (5)}}$

3. Ok so i got

$x=\frac{e^2 - 3}{-3}$

is that correct?

4. Originally Posted by Ife
Ok so i got $x=\frac{e^2 - 3}{-3}$
is that correct?
How in the world did you get anything like that.
Form what I gave you it follows that $(5-4x)=(2-x)^2$.

5. lol. oh my. i feel so dumb. this is stuff i kno. i don't know whats wrong with me this time.. thanks so much! i totally forgot about the 2. Thanks again.

6. This is an additional hint only:

Originally Posted by Ife
Solve the logarithmic equation:

From the original equation you can see that the domain is: $x \in \left(-\infty, \dfrac54\right)$

Originally Posted by Plato
...
Form what I gave you it follows that $(5-4x)=(2-x)^2$.
Originally Posted by Ife
... this is stuff i kno. ...
If you solve the equation Plato gave you you'll get 2 results. Check your solution because only one of the values of x belongs to the domain!