Precalculus Examples

$e^{5 x - 3} - 2 = 10476$

Step 1

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

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Step 1.1

Add $2$ to both sides of the equation.

$e^{5 x - 3} = 10476 + 2$

Step 1.2

Add $10476$ and $2$ .

$e^{5 x - 3} = 10478$

Step 2

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

$\ln (e^{5 x - 3}) = \ln (10478)$

Step 3

Expand the left side.

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Step 3.1

Expand $\ln (e^{5 x - 3})$ by moving $5 x - 3$ outside the logarithm.

$(5 x - 3) \ln (e) = \ln (10478)$

Step 3.2

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

$(5 x - 3) \cdot 1 = \ln (10478)$

Step 3.3

Multiply $5 x - 3$ by $1$ .

$5 x - 3 = \ln (10478)$

Step 4

Add $3$ to both sides of the equation.

$5 x = \ln (10478) + 3$

Step 5

Divide each term in $5 x = \ln (10478) + 3$ by $5$ and simplify.

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Step 5.1

Divide each term in $5 x = \ln (10478) + 3$ by $5$ .

$\frac{5 x}{5} = \frac{\ln (10478)}{5} + \frac{3}{5}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $5$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{\ln (10478)}{5} + \frac{3}{5}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (10478)}{5} + \frac{3}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (10478)}{5} + \frac{3}{5}$

Decimal Form:

$x = 2.45140661 \dots$