Evaluate Using the Given Value 233 , 280=5(6)^(1/3x+2)

$233$ , $280 = 5 {(6)}^{\frac{1}{3} x + 2}$

Rewrite the equation as $5 \cdot 6^{\frac{1}{3} x + 2} = 280$ .

$5 \cdot 6^{\frac{1}{3} x + 2} = 280$

Divide each term in $(5 \cdot 6^{\frac{1}{3} x + 2}) = 280$ by $5$ and simplify.

Divide each term in $(5 \cdot 6^{\frac{1}{3} x + 2}) = 280$ by $5$ .

$\frac{(5 \cdot 6^{\frac{1}{3} x + 2})}{5} = \frac{280}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 \cdot 6^{\frac{1}{3} x + 2}}{5} = \frac{280}{5}$

Divide $6^{\frac{1}{3} x + 2}$ by $1$ .

$6^{\frac{1}{3} x + 2} = \frac{280}{5}$

Combine $\frac{1}{3}$ and $x$ .

$6^{\frac{x}{3} + 2} = \frac{280}{5}$

Simplify the right side.

Divide $280$ by $5$ .

$6^{\frac{x}{3} + 2} = 56$

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

$\ln (6^{\frac{x}{3} + 2}) = \ln (56)$

Expand $\ln (6^{\frac{x}{3} + 2})$ by moving $\frac{x}{3} + 2$ outside the logarithm.

$(\frac{x}{3} + 2) \ln (6) = \ln (56)$

Simplify the left side.

Simplify $(\frac{x}{3} + 2) \ln (6)$ .

Apply the distributive property.

$\frac{x}{3} \ln (6) + 2 \ln (6) = \ln (56)$

Combine $\frac{x}{3}$ and $\ln (6)$ .

$\frac{x \ln (6)}{3} + 2 \ln (6) = \ln (56)$

Move all the terms containing a logarithm to the left side of the equation.

$\frac{x \ln (6)}{3} + 2 \ln (6) - \ln (56) = 0$

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

Subtract $2 \ln (6)$ from both sides of the equation.

$\frac{x \ln (6)}{3} - \ln (56) = - 2 \ln (6)$

Add $\ln (56)$ to both sides of the equation.

$\frac{x \ln (6)}{3} = - 2 \ln (6) + \ln (56)$

Multiply both sides of the equation by $3$ .

$3 \frac{x \ln (6)}{3} = 3 (- 2 \ln (6) + \ln (56))$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{x \ln (6)}{3} = 3 (- 2 \ln (6) + \ln (56))$

Rewrite the expression.

$x \ln (6) = 3 (- 2 \ln (6) + \ln (56))$

Simplify the right side.

Simplify $3 (- 2 \ln (6) + \ln (56))$ .

Apply the distributive property.

$x \ln (6) = 3 (- 2 \ln (6)) + 3 \ln (56)$

Multiply $- 2$ by $3$ .

$x \ln (6) = - 6 \ln (6) + 3 \ln (56)$

Divide each term in $x \ln (6) = - 6 \ln (6) + 3 \ln (56)$ by $\ln (6)$ and simplify.

Divide each term in $x \ln (6) = - 6 \ln (6) + 3 \ln (56)$ by $\ln (6)$ .

$\frac{x \ln (6)}{\ln (6)} = \frac{- 6 \ln (6)}{\ln (6)} + \frac{3 \ln (56)}{\ln (6)}$

Simplify the left side.

Cancel the common factor of $\ln (6)$ .

Cancel the common factor.

$\frac{x \ln (6)}{\ln (6)} = \frac{- 6 \ln (6)}{\ln (6)} + \frac{3 \ln (56)}{\ln (6)}$

Divide $x$ by $1$ .

$x = \frac{- 6 \ln (6)}{\ln (6)} + \frac{3 \ln (56)}{\ln (6)}$

Simplify the right side.

Cancel the common factor of $\ln (6)$ .

Cancel the common factor.

$x = \frac{- 6 \ln (6)}{\ln (6)} + \frac{3 \ln (56)}{\ln (6)}$

Divide $- 6$ by $1$ .

$x = - 6 + \frac{3 \ln (56)}{\ln (6)}$

Replace the variable $x$ with $- 6 + \frac{3 \ln (56)}{\ln (6)}$ in the expression.

$233$

Evaluate Using the Given Value 233 , 280=5(6)^(1/3x+2)

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