Final answer to the problem
$x=\frac{8+\sqrt{128}}{2},\:x=\frac{8-\sqrt{128}}{2}$
Got another answer? Verify it here!
Step-by-step Solution
How should I solve this problem?
- Choisir une option
- Résoudre pour x
- Simplifier
- Facteur
- Trouver les racines
- Load more...
Can't find a method? Tell us so we can add it.
1
Apply the formula: $a\log_{b}\left(x\right)$$=\log_{b}\left(x^a\right)$
$\log_{4}\left(\left(2-x\right)^2\right)-\log_{4}\left(x+5\right)=1$
Learn how to solve problems step by step online.
$\log_{4}\left(\left(2-x\right)^2\right)-\log_{4}\left(x+5\right)=1$
Learn how to solve problems step by step online. 2log4(2+-1*x)-log4(x+5)=1. Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right). Apply the formula: \log_{b}\left(x\right)-\log_{b}\left(y\right)=\log_{b}\left(\frac{x}{y}\right), where b=4, x=\left(2-x\right)^2 and y=x+5. Apply the formula: \left(a+b\right)^2=a^2+2ab+b^2, where a=-x, b=2 and a+b=2-x. Apply the formula: \log_{b}\left(x\right)=a\to b^{\log_{b}\left(x\right)}=b^a, where a=1, b=4 and x=\frac{x^2-4x+4}{x+5}.
Final answer to the problem
$x=\frac{8+\sqrt{128}}{2},\:x=\frac{8-\sqrt{128}}{2}$
