Algebra Examples

$e^{10 - n} + 1 = 35.4$

Step 1

Move all terms not containing $n$ to the right side of the equation.

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Step 1.1

Subtract $1$ from both sides of the equation.

$e^{10 - n} = 35.4 - 1$

Step 1.2

Subtract $1$ from $35.4$ .

$e^{10 - n} = 34.4$

Step 2

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

$\ln (e^{10 - n}) = \ln (34.4)$

Step 3

Expand the left side.

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Step 3.1

Expand $\ln (e^{10 - n})$ by moving $10 - n$ outside the logarithm.

$(10 - n) \ln (e) = \ln (34.4)$

Step 3.2

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

$(10 - n) \cdot 1 = \ln (34.4)$

Step 3.3

Multiply $10 - n$ by $1$ .

$10 - n = \ln (34.4)$

Step 4

Subtract $10$ from both sides of the equation.

$- n = \ln (34.4) - 10$

Step 5

Divide each term in $- n = \ln (34.4) - 10$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- n = \ln (34.4) - 10$ by $- 1$ .

$\frac{- n}{- 1} = \frac{\ln (34.4)}{- 1} + \frac{- 10}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{n}{1} = \frac{\ln (34.4)}{- 1} + \frac{- 10}{- 1}$

Step 5.2.2

Divide $n$ by $1$ .

$n = \frac{\ln (34.4)}{- 1} + \frac{- 10}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Move the negative one from the denominator of $\frac{\ln (34.4)}{- 1}$ .

$n = - 1 \cdot \ln (34.4) + \frac{- 10}{- 1}$

Step 5.3.1.2

Rewrite $- 1 \cdot \ln (34.4)$ as $- \ln (34.4)$ .

$n = - \ln (34.4) + \frac{- 10}{- 1}$

Step 5.3.1.3

Divide $- 10$ by $- 1$ .

$n = - \ln (34.4) + 10$

Step 6

The result can be shown in multiple forms.

Exact Form:

$n = - \ln (34.4) + 10$

Decimal Form:

$n = 6.46194343 \dots$