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# Expand the logarithmic expression $\log \left(10x^5\right)$

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ln
log
log
lim
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sin
cos
tan
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asin
acos
atan
acot
asec
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sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

## Properties of Logarithms

· Product rule
$\log_{b}\left(mn\right)=\log_{b}\left(m\right)+\log_{b}\left(n\right)$
· Power rule
$\log_{b}\left(x^a\right)=a\log_{b}\left(x\right)$

SnapXam A2

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0
a
b
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f
g
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

###  Main Topic: Expanding Logarithms

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