Basic Math Examples

$12000 \log_{2} (k) = 192000$

Step 1

Divide each term in $12000 \log_{2} (k) = 192000$ by $12000$ and simplify.

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Step 1.1

Divide each term in $12000 \log_{2} (k) = 192000$ by $12000$ .

$\frac{12000 \log_{2} (k)}{12000} = \frac{192000}{12000}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $12000$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{12000 \log_{2} (k)}{12000} = \frac{192000}{12000}$

Step 1.2.1.2

Divide $\log_{2} (k)$ by $1$ .

$\log_{2} (k) = \frac{192000}{12000}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $192000$ by $12000$ .

$\log_{2} (k) = 16$

Step 2

Rewrite $\log_{2} (k) = 16$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$2^{16} = k$

Step 3

Solve for $k$ .

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Step 3.1

Rewrite the equation as $k = 2^{16}$ .

$k = 2^{16}$

Step 3.2

Raise $2$ to the power of $16$ .

$k = 65536$