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

Step-by-step Solution

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Final answer to the problem

$2\log_{4}\left(x\right)+1$
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Step-by-step Solution

How should I solve this problem?

  • Choose an option
  • Solve for x
  • Condense the logarithm
  • Expand the logarithm
  • Simplify
  • Find the integral
  • Find the derivative
  • Write as single logarithm
  • Integrate by partial fractions
  • Product of Binomials with Common Term
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Use the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$, where $M=x^2$ and $N=4$

$\log_{4}\left(x^2\right)+\log_{4}\left(4\right)$

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

$\log_{4}\left(x^2\right)+\log_{4}\left(4\right)$

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Learn how to solve expanding logarithms problems step by step online. Expand the logarithmic expression log4(4*x^2). 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 and N=4. Evaluating the logarithm of base 4 of 4. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x).

Final answer to the problem

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

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Function Plot

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

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7
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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

How to improve your answer:

Main Topic: Expanding Logarithms

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

Used Formulas

See formulas (2)

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