Algebra Examples

$\frac{1}{2} \cdot \ln (256) - 3 \cdot \ln (2)$

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{1}{2} \ln (256)$ by moving $\frac{1}{2}$ inside the logarithm.

$\ln (256^{\frac{1}{2}}) - 3 \cdot \ln (2)$

Step 1.2

Rewrite $256$ as $16^{2}$ .

$\ln ({(16^{2})}^{\frac{1}{2}}) - 3 \cdot \ln (2)$

Step 1.3

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\ln (16^{2 (\frac{1}{2})}) - 3 \cdot \ln (2)$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Cancel the common factor.

$\ln (16^{2 (\frac{1}{2})}) - 3 \cdot \ln (2)$

Step 1.4.2

Rewrite the expression.

$\ln (16^{1}) - 3 \cdot \ln (2)$

Step 1.5

Evaluate the exponent.

$\ln (16) - 3 \cdot \ln (2)$

Step 1.6

Simplify $- 3 \ln (2)$ by moving $3$ inside the logarithm.

$\ln (16) - \ln (2^{3})$

Step 1.7

Raise $2$ to the power of $3$ .

$\ln (16) - \ln (8)$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\ln (\frac{16}{8})$

Step 3

Divide $16$ by $8$ .

$\ln (2)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\ln (2)$

Decimal Form:

$0.69314718 \dots$