Condense the logarithmic expression $\frac{\log_{x}\left(9\right)+\log_{x}\left(81\right)-\log_{x}\left(3\right)}{\log_{x}\left(2187\right)}$

Step-by-step Solution

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Final answer to the problem

$\log_{2187}\left(243\right)$
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Step-by-step Solution

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  • 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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The difference of two logarithms of equal base $b$ is equal to the logarithm of the quotient: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$

$\frac{\log_{x}\left(3\right)+\log_{x}\left(81\right)}{\log_{x}\left(2187\right)}$

Learn how to solve definite integrals problems step by step online.

$\frac{\log_{x}\left(3\right)+\log_{x}\left(81\right)}{\log_{x}\left(2187\right)}$

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Learn how to solve definite integrals problems step by step online. Condense the logarithmic expression (logx(9)+logx(81)-logx(3))/logx(2187). 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). The sum of two logarithms of the same base is equal to the logarithm of the product of the arguments. Multiply 3 times 81. Apply the change of base formula for logarithms: \log_b(a)=\frac{\log_x(a)}{\log_x(b)}.

Final answer to the problem

$\log_{2187}\left(243\right)$

Exact Numeric Answer

$0.714286$

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Plotting: $\log_{2187}\left(243\right)$

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7
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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

How to improve your answer:

Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

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