Algebra Examples

$5 - 3^{x} = - 40$

Step 1

Add $40$ to both sides of the equation.

$5 - 3^{x} + 40 = 0$

Step 2

Add $5$ and $40$ .

$45 - 3^{x} = 0$

Step 3

Subtract $45$ from both sides of the equation.

$- 3^{x} = - 45$

Step 4

Divide each term in $- 3^{x} = - 45$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- 3^{x} = - 45$ by $- 1$ .

$\frac{- 3^{x}}{- 1} = \frac{- 45}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{3^{x}}{1} = \frac{- 45}{- 1}$

Step 4.2.2

Divide $3^{x}$ by $1$ .

$3^{x} = \frac{- 45}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 45$ by $- 1$ .

$3^{x} = 45$

Step 5

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

$\ln (3^{x}) = \ln (45)$

Step 6

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

$x \ln (3) = \ln (45)$

Step 7

Divide each term in $x \ln (3) = \ln (45)$ by $\ln (3)$ and simplify.

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Step 7.1

Divide each term in $x \ln (3) = \ln (45)$ by $\ln (3)$ .

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (45)}{\ln (3)}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $\ln (3)$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (45)}{\ln (3)}$

Step 7.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (45)}{\ln (3)}$