Condense the logarithmic expression $\ln\left(\frac{x}{x-9}\right)+\ln\left(\frac{x+9}{x}\right)-\ln\left(x^2-81\right)$

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Tutorial - Condensing logarithmic expressions ex 12, 1/3(2ln(x+3)+lnx-ln(x^2-1))

https://www.youtube.com/watch?v=l8AE8UzknbY

Expanding a natural logarithmic expression

https://www.youtube.com/watch?v=F-YgwOUB0Oo

Pre-Calculus - Condensing a logarithmic expression to one logarithm 2[3lnx - ln(x+1)-ln(x-1)]

https://www.youtube.com/watch?v=HS0--oEAT4I

How to use properties of logs to expand an expression with roots

https://www.youtube.com/watch?v=IdcLlCwz4Ok

Tutorial - Condensing logarithmic expressions ex 11, 1/2(3log2(x)-2 log2(z))

https://www.youtube.com/watch?v=doNh13E4XBo

How to rewrite a logarithmic expression as one single logarithm

https://www.youtube.com/watch?v=JWI06mfSrh0

Function Plot

Plotting: $\ln\left(\frac{x+9}{\left(x-9\right)\left(x^2-81\right)}\right)$

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0
a
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m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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: Condensing Logarithms

Combining or condensing logarithms consists of rewriting a mathematical expression with several logarithms into a single logarithm, by applying the properties of logarithms.

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