Answer:
x
=
e
y
+
3
−
4
Explanation:
Algebra Examples
Popular Problems Algebra Find the Inverse y=e^(x+3)-4
y
=
e
x
+
3
−
4
Interchange the variables.
x
=
e
y
+
3
−
4
Solve for
y
.
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Since
y
is on the right side of the equation, switch the sides so it is on the left side of the equation.
e
y
+
3
−
4
=
x
Add
4
to both sides of the equation.
e
y
+
3
=
x
+
4
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln
(
e
y
+
3
)
=
ln
(
x
+
4
)
Use logarithm rules to move
y
+
3
out of the exponent.
(
y
+
3
)
ln
(
e
)
=
ln
(
x
+
4
)
The natural logarithm of
e
is
1
.
(
y
+
3
)
⋅
1
=
ln
(
x
+
4
)
Multiply
y
+
3
by
1
.
y
+
3
=
ln
(
x
+
4
)
Subtract
3
from both sides of the equation.