Finite Math Examples

$f (x) = 3 x + 6 \ln (6)$

Step 1

Set $3 x + 6 \ln (6)$ equal to $0$ .

$3 x + 6 \ln (6) = 0$

Step 2

Solve for $x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Simplify $6 \ln (6)$ by moving $6$ inside the logarithm.

$3 x + \ln (6^{6}) = 0$

Step 2.1.2

Raise $6$ to the power of $6$ .

$3 x + \ln (46656) = 0$

Step 2.2

Subtract $\ln (46656)$ from both sides of the equation.

$3 x = - \ln (46656)$

Step 2.3

Divide each term in $3 x = - \ln (46656)$ by $3$ and simplify.

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Step 2.3.1

Divide each term in $3 x = - \ln (46656)$ by $3$ .

$\frac{3 x}{3} = \frac{- \ln (46656)}{3}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $3$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- \ln (46656)}{3}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \ln (46656)}{3}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Move the negative in front of the fraction.

$x = - \frac{\ln (46656)}{3}$

Step 2.3.3.2

Rewrite $\frac{\ln (46656)}{3}$ as $\frac{1}{3} \ln (46656)$ .

$x = - (\frac{1}{3} \ln (46656))$

Step 2.3.3.3

Simplify $\frac{1}{3} \ln (46656)$ by moving $\frac{1}{3}$ inside the logarithm.

$x = - \ln (46656^{\frac{1}{3}})$

Step 2.3.3.4

Simplify the expression.

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Step 2.3.3.4.1

Rewrite $46656$ as $36^{3}$ .

$x = - \ln ({(36^{3})}^{\frac{1}{3}})$

Step 2.3.3.4.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = - \ln (36^{3 (\frac{1}{3})})$

Step 2.3.3.5

Cancel the common factor of $3$ .

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Step 2.3.3.5.1

Cancel the common factor.

$x = - \ln (36^{3 (\frac{1}{3})})$

Step 2.3.3.5.2

Rewrite the expression.

$x = - \ln (36^{1})$

Step 2.3.3.6

Evaluate the exponent.

$x = - \ln (36)$

Step 3