Basic Math Examples

$2^{m} - 2^{n} = 56$

Step 1

Add $2^{n}$ to both sides of the equation.

$2^{m} = 56 + 2^{n}$

Step 2

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

$\ln (2^{m}) = \ln (56 + 2^{n})$

Step 3

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

$m \ln (2) = \ln (56 + 2^{n})$

Step 4

Divide each term in $m \ln (2) = \ln (56 + 2^{n})$ by $\ln (2)$ and simplify.

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Step 4.1

Divide each term in $m \ln (2) = \ln (56 + 2^{n})$ by $\ln (2)$ .

$\frac{m \ln (2)}{\ln (2)} = \frac{\ln (56 + 2^{n})}{\ln (2)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

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

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Step 4.2.1.1

Cancel the common factor.

$\frac{m \ln (2)}{\ln (2)} = \frac{\ln (56 + 2^{n})}{\ln (2)}$

Step 4.2.1.2

Divide $m$ by $1$ .

$m = \frac{\ln (56 + 2^{n})}{\ln (2)}$