Precalculus Examples

$6 \log (\frac{1}{72 d^{4}})$

Step 1

Simplify $6 \log (\frac{1}{72 d^{4}})$ by moving $6$ inside the logarithm.

$\log ({(\frac{1}{72 d^{4}})}^{6})$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 2.1

Apply the product rule to $\frac{1}{72 d^{4}}$ .

$\log (\frac{1^{6}}{{(72 d^{4})}^{6}})$

Step 2.2

Apply the product rule to $72 d^{4}$ .

$\log (\frac{1^{6}}{72^{6} {(d^{4})}^{6}})$

Step 3

One to any power is one.

$\log (\frac{1}{72^{6} {(d^{4})}^{6}})$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

Raise $72$ to the power of $6$ .

$\log (\frac{1}{139314069504 {(d^{4})}^{6}})$

Step 4.2

Multiply the exponents in ${(d^{4})}^{6}$ .

Tap for more steps...

Step 4.2.1

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

$\log (\frac{1}{139314069504 d^{4 \cdot 6}})$

Step 4.2.2

Multiply $4$ by $6$ .

$\log (\frac{1}{139314069504 d^{24}})$