Algebra Examples

e^{x - 1} - 5 = 5

$e^{x - 1} - 5 = 5$

Step 1

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 1.1

Add

5

$5$ to both sides of the equation.

e^{x - 1} = 5 + 5

$e^{x - 1} = 5 + 5$

Step 1.2

Add

5

$5$ and

5

$5$ .

e^{x - 1} = 10

$e^{x - 1} = 10$

e^{x - 1} = 10

$e^{x - 1} = 10$

Step 2

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

\ln (e^{x - 1}) = \ln (10)

$\ln (e^{x - 1}) = \ln (10)$

Step 3

Expand the left side.

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Step 3.1

Expand

\ln (e^{x - 1})

$\ln (e^{x - 1})$ by moving

x - 1

$x - 1$ outside the logarithm.

(x - 1) \ln (e) = \ln (10)

$(x - 1) \ln (e) = \ln (10)$

Step 3.2

The natural logarithm of

e

$e$ is

1

$1$ .

(x - 1) \cdot 1 = \ln (10)

$(x - 1) \cdot 1 = \ln (10)$

Step 3.3

Multiply

x - 1

$x - 1$ by

1

$1$ .

x - 1 = \ln (10)

$x - 1 = \ln (10)$

x - 1 = \ln (10)

$x - 1 = \ln (10)$

Step 4

Add

1

$1$ to both sides of the equation.

x = \ln (10) + 1

$x = \ln (10) + 1$

Step 5

The result can be shown in multiple forms.

Exact Form:

x = \ln (10) + 1

$x = \ln (10) + 1$

Decimal Form:

x = 3.30258509 \dots

$x = 3.30258509 \dots$

e^{x - 1} - 5 = 5

$e^{x - 1} - 5 = 5$

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