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

# Solve the logarithmic equation $\log \left(x^2\right)-\log \left(x\right)=3$

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

The equation has no solutions.

##  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

The difference of two logarithms of equal base $b$ is equal to the logarithm of the quotient: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$

$\log \left(\frac{x^2}{x}\right)=3$

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

$\log \left(\frac{x^2}{x}\right)=3$

Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation log(x^2)-log(x)=3. The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right). Simplify the fraction \frac{x^2}{x} by x. Express the numbers in the equation as logarithms of base 10. For two logarithms of the same base to be equal, their arguments must be equal. In other words, if \log(a)=\log(b) then a must equal b.

##  Final answer to the problem

The equation has no solutions.

##  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

###  Main Topic: Logarithmic Equations

Are those equations in which the unknown variable appears within a logarithm.