Solve for x 2.1 = natural log of 6x

$2.1 = \ln (6 x)$

Step 1

Rewrite the equation as $\ln (6 x) = 2.1$ .

$\ln (6 x) = 2.1$

Step 2

To solve for $x$ , rewrite the equation using properties of logarithms.

$e^{\ln (6 x)} = e^{2.1}$

Step 3

Rewrite $\ln (6 x) = 2.1$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$e^{2.1} = 6 x$

Step 4

Solve for $x$ .

Rewrite the equation as $6 x = e^{2.1}$ .

$6 x = e^{2.1}$

Divide each term in $6 x = e^{2.1}$ by $6$ and simplify.

Divide each term in $6 x = e^{2.1}$ by $6$ .

$\frac{6 x}{6} = \frac{e^{2.1}}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{e^{2.1}}{6}$

Divide $x$ by $1$ .

$x = \frac{e^{2.1}}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{e^{2.1}}{6}$

Decimal Form:

$x = 1.36102831 \dots$

Solve for x 2.1 = natural log of 6x

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