Basic Math Examples

$\frac{1}{2^{c}} = 0.875$

Step 1

Multiply both sides by $2^{c}$ .

$\frac{1}{2^{c}} \cdot 2^{c} = 0.875 \cdot 2^{c}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $2^{c}$ .

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Step 2.1.1

Cancel the common factor.

$\frac{1}{2^{c}} \cdot 2^{c} = 0.875 \cdot 2^{c}$

Step 2.1.2

Rewrite the expression.

$1 = 0.875 \cdot 2^{c}$

Step 3

Solve for $c$ .

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Step 3.1

Rewrite the equation as $0.875 \cdot 2^{c} = 1$ .

$0.875 \cdot 2^{c} = 1$

Step 3.2

Divide each term in $0.875 \cdot 2^{c} = 1$ by $0.875$ and simplify.

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Step 3.2.1

Divide each term in $0.875 \cdot 2^{c} = 1$ by $0.875$ .

$\frac{0.875 \cdot 2^{c}}{0.875} = \frac{1}{0.875}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $0.875$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{0.875 \cdot 2^{c}}{0.875} = \frac{1}{0.875}$

Step 3.2.2.1.2

Divide $2^{c}$ by $1$ .

$2^{c} = \frac{1}{0.875}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $1$ by $0.875$ .

$2^{c} = 1.\overline{142857}$

Step 3.3

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

$\ln (2^{c}) = \ln (1.\overline{142857})$

Step 3.4

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

$c \ln (2) = \ln (1.\overline{142857})$

Step 3.5

Divide each term in $c \ln (2) = \ln (1.\overline{142857})$ by $\ln (2)$ and simplify.

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Step 3.5.1

Divide each term in $c \ln (2) = \ln (1.\overline{142857})$ by $\ln (2)$ .

$\frac{c \ln (2)}{\ln (2)} = \frac{\ln (1.\overline{142857})}{\ln (2)}$

Step 3.5.2

Simplify the left side.

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Step 3.5.2.1

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

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Step 3.5.2.1.1

Cancel the common factor.

$\frac{c \ln (2)}{\ln (2)} = \frac{\ln (1.\overline{142857})}{\ln (2)}$

Step 3.5.2.1.2

Divide $c$ by $1$ .

$c = \frac{\ln (1.\overline{142857})}{\ln (2)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$c = \frac{\ln (1.\overline{142857})}{\ln (2)}$

Decimal Form:

$c = 0.19264507 \dots$