Basic Math Examples

$5 {(2)}^{3 y} - 4 = 13$

Step 1

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

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Step 1.1

Add $4$ to both sides of the equation.

$5 \cdot 2^{3 y} = 13 + 4$

Step 1.2

Add $13$ and $4$ .

$5 \cdot 2^{3 y} = 17$

Step 2

Divide each term in $5 \cdot 2^{3 y} = 17$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 \cdot 2^{3 y} = 17$ by $5$ .

$\frac{5 \cdot 2^{3 y}}{5} = \frac{17}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 \cdot 2^{3 y}}{5} = \frac{17}{5}$

Step 2.2.1.2

Divide $2^{3 y}$ by $1$ .

$2^{3 y} = \frac{17}{5}$

Step 3

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

$\ln (2^{3 y}) = \ln (\frac{17}{5})$

Step 4

Expand $\ln (2^{3 y})$ by moving $3 y$ outside the logarithm.

$3 y \ln (2) = \ln (\frac{17}{5})$

Step 5

Divide each term in $3 y \ln (2) = \ln (\frac{17}{5})$ by $3 \ln (2)$ and simplify.

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Step 5.1

Divide each term in $3 y \ln (2) = \ln (\frac{17}{5})$ by $3 \ln (2)$ .

$\frac{3 y \ln (2)}{3 \ln (2)} = \frac{\ln (\frac{17}{5})}{3 \ln (2)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 y \ln (2)}{3 \ln (2)} = \frac{\ln (\frac{17}{5})}{3 \ln (2)}$

Step 5.2.1.2

Rewrite the expression.

$\frac{y \ln (2)}{\ln (2)} = \frac{\ln (\frac{17}{5})}{3 \ln (2)}$

Step 5.2.2

Cancel the common factor of $\ln (2)$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{y \ln (2)}{\ln (2)} = \frac{\ln (\frac{17}{5})}{3 \ln (2)}$

Step 5.2.2.2

Divide $y$ by $1$ .

$y = \frac{\ln (\frac{17}{5})}{3 \ln (2)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{\ln (\frac{17}{5})}{3 \ln (2)}$

Decimal Form:

$y = 0.58851158 \dots$