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Expand the logarithmic expression $\log_{2}\left(x^4-1\right)$

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Solution

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Final Answer

$\log_{2}\left(x^{2}+1\right)+\log_{2}\left(x+1\right)+\log_{2}\left(x-1\right)$
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Step-by-step Solution

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Factor the difference of squares $x^4-1$ as the product of two conjugated binomials

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

Learn how to solve expanding logarithms problems step by step online.

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

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Learn how to solve expanding logarithms problems step by step online. Expand the logarithmic expression log2(x^4+-1). Factor the difference of squares x^4-1 as the product of two conjugated binomials. Use the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right), where M=x^{2}+1 and N=x^{2}-1. Factor the difference of squares x^{2}-1 as the product of two conjugated binomials. Use the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right), where M=x+1 and N=x-1.

Final Answer

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

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SimplifyWrite as single logarithmCondense the logarithmExpand the logarithmFind the integralFind the derivativeSolve for x

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Function Plot

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

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a
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g
m
n
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x
y
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.
(◻)
+
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×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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: Expanding Logarithms

Logarithm expansion consists of applying the properties of logarithms to express a single logarithm in multiple logarithms, usually much simpler.

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