ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Solve the logarithmic equation $\log_{x}\left(64\right)=3$

Go!
Symbolic mode
Text mode
Go!
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

##  Final answer to the problem

$x=4$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Solve for x
• Find the derivative using the definition
• Solve by quadratic formula (general formula)
• Simplify
• Find the integral
• Find the derivative
• Factor
• Factor by completing the square
• Find the roots
Can't find a method? Tell us so we can add it.
1

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

$\frac{\log_{64}\left(64\right)}{\log_{64}\left(x\right)}=3$

Learn how to solve problems step by step online.

$\frac{\log_{64}\left(64\right)}{\log_{64}\left(x\right)}=3$

Learn how to solve problems step by step online. Solve the logarithmic equation logx(64)=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

$x=4$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

Go!
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