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Solve the logarithmic equation $\log_{x}\left(8\right)=3$

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Solution

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Final answer to the problem

$x=2$
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Step-by-step Solution

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1

Change the logarithm to base $x$ applying the change of base formula for logarithms: $\log_b(a)=\frac{\log_x(a)}{\log_x(b)}$

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

$\frac{\log_{8}\left(8\right)}{\log_{8}\left(x\right)}=3$

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Unlock the first 3 steps of this solution

Learn how to solve logarithmic differentiation problems step by step online. Solve the logarithmic equation logx(8)=3. Change the logarithm to base x applying the change of base formula for logarithms: \log_b(a)=\frac{\log_x(a)}{\log_x(b)}. If the argument of the logarithm (inside the parenthesis) and the base are equal, then the logarithm equals 1. Take the reciprocal of both sides of the equation. Any expression divided by one (1) is equal to that same expression.

Final answer to the problem

$x=2$

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Function Plot

Plotting: $\log_{x}\left(8\right)-3$

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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
D□x
∫
∫◻
|◻|
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:

Similar Problems Solved

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$\log_x\left(\frac{1}{8}\right)=-3$

$\log_x\left(100\right)-\log_x\left(25\right)=2$

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$\log\left(\left(y+2\right)\right)=1+\log\left(\left(2y-6\right)\right)$

Main Topic: Logarithmic Differentiation

The logarithmic derivative of a function f(x) is defined by the formula f'(x)/f(x).

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