Basic Math Examples

$(9.1) e^{y} = 2.4$

Step 1

Divide each term in $9.1 e^{y} = 2.4$ by $9.1$ and simplify.

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Step 1.1

Divide each term in $9.1 e^{y} = 2.4$ by $9.1$ .

$\frac{9.1 e^{y}}{9.1} = \frac{2.4}{9.1}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $9.1$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{9.1 e^{y}}{9.1} = \frac{2.4}{9.1}$

Step 1.2.1.2

Divide $e^{y}$ by $1$ .

$e^{y} = \frac{2.4}{9.1}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $2.4$ by $9.1$ .

$e^{y} = 0.\overline{263736}$

Step 2

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

$\ln (e^{y}) = \ln (0.\overline{263736})$

Step 3

Expand the left side.

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Step 3.1

Expand $\ln (e^{y})$ by moving $y$ outside the logarithm.

$y \ln (e) = \ln (0.\overline{263736})$

Step 3.2

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

$y \cdot 1 = \ln (0.\overline{263736})$

Step 3.3

Multiply $y$ by $1$ .

$y = \ln (0.\overline{263736})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \ln (0.\overline{263736})$

Decimal Form:

$y = - 1.33280567 \dots$