Algebra Examples

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

Step 1

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

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

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

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

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

Step 2.2.2

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

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

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Divide $280$ by $5$ .

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

Step 3

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

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

Step 4

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

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

Step 5

Simplify the left side.

Tap for more steps...

Step 5.1

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

Tap for more steps...

Step 5.1.1

Apply the distributive property.

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

Step 5.1.2

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

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

Step 6

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

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

Step 7

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

Tap for more steps...

Step 7.1

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

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

Step 7.2

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

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

Step 8

Multiply both sides of the equation by $3$ .

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

Step 9

Simplify both sides of the equation.

Tap for more steps...

Step 9.1

Simplify the left side.

Tap for more steps...

Step 9.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 9.1.1.1

Cancel the common factor.

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

Step 9.1.1.2

Rewrite the expression.

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

Step 9.2

Simplify the right side.

Tap for more steps...

Step 9.2.1

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

Tap for more steps...

Step 9.2.1.1

Apply the distributive property.

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

Step 9.2.1.2

Multiply $- 2$ by $3$ .

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

Step 10

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

Tap for more steps...

Step 10.1

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

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

Step 10.2

Simplify the left side.

Tap for more steps...

Step 10.2.1

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

Tap for more steps...

Step 10.2.1.1

Cancel the common factor.

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

Step 10.2.1.2

Divide $x$ by $1$ .

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

Step 10.3

Simplify the right side.

Tap for more steps...

Step 10.3.1

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

Tap for more steps...

Step 10.3.1.1

Cancel the common factor.

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

Step 10.3.1.2

Divide $- 6$ by $1$ .

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

Step 11

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

$233$