Solve the logarithmic equation $z=\ln\left(xy\right)$

Step-by-step Solution

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e
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ln
log
log
lim
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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

$y=e^{\left(z-\ln\left(x\right)\right)}$
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Step-by-step Solution

How should I solve this problem?

  • Choose an option
  • Solve for z
  • Solve for x
  • Solve for y
  • Simplify
  • Factor
  • Factor by completing the square
  • Find the integral
  • Find the derivative
  • Find the derivative using the definition
  • Load more...
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Rearrange the equation

$\ln\left(xy\right)=z$

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

$\ln\left(xy\right)=z$

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Unlock the first 3 steps of this solution

Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation z=ln(xy). Rearrange the equation. Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). We need to isolate the dependent variable y, we can do that by simultaneously subtracting \ln\left(x\right) from both sides of the equation. Take the variable outside of the logarithm.

Final answer to the problem

$y=e^{\left(z-\ln\left(x\right)\right)}$

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Function Plot

Plotting: $z-\ln\left(xy\right)$

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Got a different answer? Verify it!

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

How to improve your answer:

Main Topic: Logarithmic Equations

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

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