Solve the logarithmic equation $\log_{2}\left(x+3\right)=5-\log_{2}\left(x-1\right)$

Step-by-step Solution

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Final answer to the problem

$x=5$
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Step-by-step Solution

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Express the numbers in the equation as logarithms of base $2$

$\log_{2}\left(x+3\right)=\log_{2}\left(2^{5}\right)-\log_{2}\left(x-1\right)$

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$\log_{2}\left(x+3\right)=\log_{2}\left(2^{5}\right)-\log_{2}\left(x-1\right)$

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Learn how to solve problems step by step online. Solve the logarithmic equation log2(x+3)=5-log2(x+-1). Express the numbers in the equation as logarithms of base 2. The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right). For two logarithms of the same base to be equal, their arguments must be equal. In other words, if \log(a)=\log(b) then a must equal b. We need to isolate the dependent variable x, we can do that by simultaneously subtracting 3 from both sides of the equation.

Final answer to the problem

$x=5$

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Function Plot

Plotting: $\log_{2}\left(x+3\right)-5+\log_{2}\left(x-1\right)$

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5
6
7
8
9
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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