Algebra Examples

e^{x} = 0.5

$e^{x} = 0.5$

Step 1

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

\ln (e^{x}) = \ln (0.5)

$\ln (e^{x}) = \ln (0.5)$

Step 2

Expand the left side.

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Step 2.1

Expand

\ln (e^{x})

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

x

$x$ outside the logarithm.

x \ln (e) = \ln (0.5)

$x \ln (e) = \ln (0.5)$

Step 2.2

The natural logarithm of

e

$e$ is

1

$1$ .

x \cdot 1 = \ln (0.5)

$x \cdot 1 = \ln (0.5)$

Step 2.3

Multiply

x

$x$ by

1

$1$ .

x = \ln (0.5)

$x = \ln (0.5)$

x = \ln (0.5)

$x = \ln (0.5)$

Step 3

The result can be shown in multiple forms.

Exact Form:

x = \ln (0.5)

$x = \ln (0.5)$

Decimal Form:

x = - 0.69314718 \dots

$x = - 0.69314718 \dots$

e^{x} = 0.5

$e^{x} = 0.5$

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