Finite Math Examples

$\log (2^{50}) = \frac{\log (e^{50})}{\log (e^{2})}$

Step 1

Raise $2$ to the power of $50$ .

$\log (1125899906842620) = \frac{\log (e^{50})}{\log (e^{2})}$

Step 2

Simplify $\frac{\log (e^{50})}{\log (e^{2})}$ .

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Step 2.1

Expand $\log (e^{50})$ by moving $50$ outside the logarithm.

$\log (1125899906842620) = \frac{50 \log (e)}{\log (e^{2})}$

Step 2.2

Expand $\log (e^{2})$ by moving $2$ outside the logarithm.

$\log (1125899906842620) = \frac{50 \log (e)}{2 \log (e)}$

Step 2.3

Cancel the common factor of $50$ and $2$ .

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Step 2.3.1

Factor $2$ out of $50 \log (e)$ .

$\log (1125899906842620) = \frac{2 (25 \log (e))}{2 \log (e)}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $2$ out of $2 \log (e)$ .

$\log (1125899906842620) = \frac{2 (25 \log (e))}{2 (\log (e))}$

Step 2.3.2.2

Cancel the common factor.

$\log (1125899906842620) = \frac{2 (25 \log (e))}{2 \log (e)}$

Step 2.3.2.3

Rewrite the expression.

$\log (1125899906842620) = \frac{25 \log (e)}{\log (e)}$

Step 2.4

Cancel the common factor of $\log (e)$ .

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Step 2.4.1

Cancel the common factor.

$\log (1125899906842620) = \frac{25 \log (e)}{\log (e)}$

Step 2.4.2

Divide $25$ by $1$ .

$\log (1125899906842620) = 25$

Step 3