What is expand log_{4}((2w^4)^3) ?

The solution to expand log_{4}((2w^4)^3) is 3/2+12log_{4}(w)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand log_{4}((2w^4)^3)

expand

lo g_{4} ((2 w^{4})^{3})

\frac{3}{2} + 12 lo g_{4} (w)

Solution steps

lo g_{4} ((2 w^{4})^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{4} ((2 w^{4})^{3}) = 3 lo g_{4} (2 w^{4})

= 3 lo g_{4} (2 w^{4})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

3 lo g_{4} (2 w^{4}) = 3 lo g_{4} (2) + 3 lo g_{4} (w^{4})

= 3 lo g_{4} (2) + 3 lo g_{4} (w^{4})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{4} (w^{4}) = 4 lo g_{4} (w)

= 3 lo g_{4} (2) + 3 \cdot 4 lo g_{4} (w)

Multiply the numbers:

3 \cdot 4 = 12

= 3 lo g_{4} (2) + 12 lo g_{4} (w)

3 lo g_{4} (2) = \frac{3}{2}

= \frac{3}{2} + 12 lo g_{4} (w)

ln (x) + ln (10)

ln (x) + ln (12)

lo g_{6} (6 x)

lo g_{4} (x y^{6} z^{4})

lo g_{10} (\frac{( 100 x ) ^{2}}{27})

What is expand log_{4}((2w^4)^3) ?
The solution to expand log_{4}((2w^4)^3) is 3/2+12log_{4}(w)