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

Step-by-step Solution

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Final answer to the problem

$x=\frac{7}{2}$
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Step-by-step Solution

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1

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

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

Learn how to solve equazioni logaritmiche problems step by step online.

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

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Learn how to solve equazioni logaritmiche problems step by step online. log2(2*x+1)=3. Express the numbers in the equation as logarithms of base 2. Apply the formula: \log_{a}\left(x\right)=\log_{a}\left(y\right)\to x=y, where a=2, x=2x+1 and y=2^{3}. Apply the formula: a^b=a^b, where a=2, b=3 and a^b=2^{3}. Apply the formula: x+a=b\to x+a-a=b-a, where a=1, b=8, x+a=b=2x+1=8, x=2x and x+a=2x+1.

Final answer to the problem

$x=\frac{7}{2}$

Exact Numeric Answer

$x=3.5$

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Function Plot

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

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0
a
b
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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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Main Topic: Equazioni logaritmiche

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