Precalculus Examples

$\frac{7}{2} \cdot (\log (7) (z - 4))$

Step 1

Apply the distributive property.

$\frac{7}{2} \cdot (\log (7) z + \log (7) \cdot - 4)$

Step 2

Multiply $\log (7) \cdot - 4$ .

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Step 2.1

Reorder $\log (7)$ and $- 4$ .

$\frac{7}{2} \cdot (\log (7) z - 4 \cdot \log (7))$

Step 2.2

Simplify $- 4 \cdot \log (7)$ by moving $4$ inside the logarithm.

$\frac{7}{2} \cdot (\log (7) z - \log (7^{4}))$

Step 3

Raise $7$ to the power of $4$ .

$\frac{7}{2} \cdot (\log (7) z - \log (2401))$

Step 4

Apply the distributive property.

$\frac{7}{2} (\log (7) z) + \frac{7}{2} (- \log (2401))$

Step 5

Multiply $\frac{7}{2} (\log (7) z)$ .

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Step 5.1

Reorder $\log (7)$ and $\frac{7}{2}$ .

$\frac{7}{2} \log (7) z + \frac{7}{2} (- \log (2401))$

Step 5.2

Simplify $\frac{7}{2} \log (7)$ by moving $\frac{7}{2}$ inside the logarithm.

$\log (7^{\frac{7}{2}}) z + \frac{7}{2} (- \log (2401))$

Step 6

Simplify $\frac{7}{2} \log (2401)$ by moving $\frac{7}{2}$ inside the logarithm.

$\log (7^{\frac{7}{2}}) z - \log (2401^{\frac{7}{2}})$

Step 7

Simplify each term.

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Step 7.1

Rewrite $2401$ as $49^{2}$ .

$\log (7^{\frac{7}{2}}) z - \log ({(49^{2})}^{\frac{7}{2}})$

Step 7.2

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

$\log (7^{\frac{7}{2}}) z - \log (49^{2 (\frac{7}{2})})$

Step 7.3

Cancel the common factor of $2$ .

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Step 7.3.1

Cancel the common factor.

$\log (7^{\frac{7}{2}}) z - \log (49^{2 (\frac{7}{2})})$

Step 7.3.2

Rewrite the expression.

$\log (7^{\frac{7}{2}}) z - \log (49^{7})$

Step 7.4

Raise $49$ to the power of $7$ .

$\log (7^{\frac{7}{2}}) z - \log (678223072849)$

Step 8

Reorder factors in $\log (7^{\frac{7}{2}}) z - \log (678223072849)$ .

$z \log (7^{\frac{7}{2}}) - \log (678223072849)$