Algebra Examples

$6 \ln (e) = e^{\ln (2 x)}$

Step 1

Rewrite the equation as $e^{\ln (2 x)} = 6 \ln (e)$ .

$e^{\ln (2 x)} = 6 \ln (e)$

Step 2

Solve for $x$ .

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Step 2.1

Exponentiation and log are inverse functions.

$2 x = 6 \ln (e)$

Step 2.2

Simplify $6 \ln (e)$ .

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Step 2.2.1

The natural logarithm of $e$ is $1$ .

$2 x = 6 \cdot 1$

Step 2.2.2

Multiply $6$ by $1$ .

$2 x = 6$

Step 2.3

Divide each term in $2 x = 6$ by $2$ and simplify.

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Step 2.3.1

Divide each term in $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $2$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $6$ by $2$ .

$x = 3$