Determine the equation of the inverse of y = ex+3.4

x

=

e

y

+

3

-

4

Step-by-step 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.