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Solve the logarithmic equation $y=\log_{5}\left(\frac{1}{2}x^{-4}+\sqrt[5]{x}+1\right)$

Step-by-step Solution

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Final answer to the problem

$y=\log_{5}\left(\frac{1+2\sqrt[5]{x^{21}}+2x^{4}}{2x^{4}}\right)$
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Step-by-step Solution

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Change the logarithm to base $10$ applying the change of base formula for logarithms: $\log_b(a)=\frac{\log_{10}(a)}{\log_{10}(b)}$. Since $\log_{10}(b)=\log(b)$, we don't need to write the $10$ as base

$y=\frac{\log \left(\frac{1}{2}x^{-4}+\sqrt[5]{x}+1\right)}{\log \left(5\right)}$

Learn how to solve logarithmic equations problems step by step online.

$y=\frac{\log \left(\frac{1}{2}x^{-4}+\sqrt[5]{x}+1\right)}{\log \left(5\right)}$

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Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation y=log5(0.5*x^(-4)+x^0.2+1). Change the logarithm to base 10 applying the change of base formula for logarithms: \log_b(a)=\frac{\log_{10}(a)}{\log_{10}(b)}. Since \log_{10}(b)=\log(b), we don't need to write the 10 as base. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Combine all terms into a single fraction with 2x^{4} as common denominator. When multiplying exponents with same base we can add the exponents.

Final answer to the problem

$y=\log_{5}\left(\frac{1+2\sqrt[5]{x^{21}}+2x^{4}}{2x^{4}}\right)$

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Function Plot

Plotting: $y-\log_{5}\left(\frac{1}{2}x^{-4}+\sqrt[5]{x}+1\right)$

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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: Logarithmic Equations

Are those equations in which the unknown variable appears within a logarithm.

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