Algebra Examples

e^{x} = 9

$e^{x} = 9$

Step 1

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

ln (e^{x}) = ln (9)

$\ln (e^{x}) = \ln (9)$

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 (9)

$x \ln (e) = \ln (9)$

Step 2.2

The natural logarithm of

e

$e$ is

1

$1$ .

x \cdot 1 = ln (9)

$x \cdot 1 = \ln (9)$

Step 2.3

Multiply

x

$x$ by

1

$1$ .

x = ln (9)

$x = \ln (9)$

x = ln (9)

$x = \ln (9)$

Step 3

The result can be shown in multiple forms.

Exact Form:

x = ln (9)

$x = \ln (9)$

Decimal Form:

x = 2.19722457 \dots

$x = 2.19722457 \dots$

$e^{x} = 9$

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