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Find the logarithm of $12$ to the base $5$ using change of base

Step-by-step Solution

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Final Answer

$\frac{\log \left(12\right)}{0.699}$
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Step-by-step Solution

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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

$\frac{\log \left(12\right)}{\log \left(5\right)}$
2

Evaluating the logarithm of base $10$ of $5$

$\frac{\log \left(12\right)}{0.699}$

Final Answer

$\frac{\log \left(12\right)}{0.699}$

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Function Plot

Plotting: $\frac{\log \left(12\right)}{0.699}$

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1
2
3
4
5
6
7
8
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: Base change formula of logarithms

Find logarithms when the base is different from $10$, using the base change formula: $\log_a(x)=\frac{\log_{10}(x)}{\log_{10}(a)}$.

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