Basic Math Examples

$6400 = 2^{y}$

Step 1

Rewrite the equation as $2^{y} = 6400$ .

$2^{y} = 6400$

Step 2

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

$\ln (2^{y}) = \ln (6400)$

Step 3

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

$y \ln (2) = \ln (6400)$

Step 4

Divide each term in $y \ln (2) = \ln (6400)$ by $\ln (2)$ and simplify.

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Step 4.1

Divide each term in $y \ln (2) = \ln (6400)$ by $\ln (2)$ .

$\frac{y \ln (2)}{\ln (2)} = \frac{\ln (6400)}{\ln (2)}$

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.

$\frac{y \ln (2)}{\ln (2)} = \frac{\ln (6400)}{\ln (2)}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{\ln (6400)}{\ln (2)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{\ln (6400)}{\ln (2)}$

Decimal Form:

$y = 12.64385618 \dots$