Basic Math Examples

$9875 = \frac{35}{5} \cdot {(1 + 5)}^{12 \cdot y} - 1$

Step 1

Rewrite the equation as $\frac{35}{5} \cdot {(1 + 5)}^{12 \cdot y} - 1 = 9875$ .

$\frac{35}{5} \cdot {(1 + 5)}^{12 \cdot y} - 1 = 9875$

Step 2

Simplify each term.

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Step 2.1

Divide $35$ by $5$ .

$7 \cdot {(1 + 5)}^{12 \cdot y} - 1 = 9875$

Step 2.2

Add $1$ and $5$ .

$7 \cdot 6^{12 y} - 1 = 9875$

Step 3

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

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Step 3.1

Add $1$ to both sides of the equation.

$7 \cdot 6^{12 y} = 9875 + 1$

Step 3.2

Add $9875$ and $1$ .

$7 \cdot 6^{12 y} = 9876$

Step 4

Divide each term in $7 \cdot 6^{12 y} = 9876$ by $7$ and simplify.

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Step 4.1

Divide each term in $7 \cdot 6^{12 y} = 9876$ by $7$ .

$\frac{7 \cdot 6^{12 y}}{7} = \frac{9876}{7}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $7$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{7 \cdot 6^{12 y}}{7} = \frac{9876}{7}$

Step 4.2.1.2

Divide $6^{12 y}$ by $1$ .

$6^{12 y} = \frac{9876}{7}$

Step 5

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

$\ln (6^{12 y}) = \ln (\frac{9876}{7})$

Step 6

Expand $\ln (6^{12 y})$ by moving $12 y$ outside the logarithm.

$12 y \ln (6) = \ln (\frac{9876}{7})$

Step 7

Divide each term in $12 y \ln (6) = \ln (\frac{9876}{7})$ by $12 \ln (6)$ and simplify.

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Step 7.1

Divide each term in $12 y \ln (6) = \ln (\frac{9876}{7})$ by $12 \ln (6)$ .

$\frac{12 y \ln (6)}{12 \ln (6)} = \frac{\ln (\frac{9876}{7})}{12 \ln (6)}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $12$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{12 y \ln (6)}{12 \ln (6)} = \frac{\ln (\frac{9876}{7})}{12 \ln (6)}$

Step 7.2.1.2

Rewrite the expression.

$\frac{y \ln (6)}{\ln (6)} = \frac{\ln (\frac{9876}{7})}{12 \ln (6)}$

Step 7.2.2

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

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Step 7.2.2.1

Cancel the common factor.

$\frac{y \ln (6)}{\ln (6)} = \frac{\ln (\frac{9876}{7})}{12 \ln (6)}$

Step 7.2.2.2

Divide $y$ by $1$ .

$y = \frac{\ln (\frac{9876}{7})}{12 \ln (6)}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$y = \frac{\ln (\frac{9876}{7})}{12 \ln (6)}$

Decimal Form:

$y = 0.33728265 \dots$