$2\log_{4}\left(2-x\right)-\log_{4}\left(x+5\right)=1$

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Final answer to the problem

$x=\frac{8+\sqrt{128}}{2},\:x=\frac{8-\sqrt{128}}{2}$
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Step-by-step Solution

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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 classificare le espressioni algebriche problems step by step online.

$\log_{4}\left(\left(2-x\right)^2\right)-\log_{4}\left(x+5\right)=1$

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Learn how to solve classificare le espressioni algebriche 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

$x=\frac{8+\sqrt{128}}{2},\:x=\frac{8-\sqrt{128}}{2}$

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Function Plot

Plotting: $2\log_{4}\left(2-x\right)-\log_{4}\left(x+5\right)-1$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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