What is expand log_{10}((2x^5)/((7+x)^4)) ?

The solution to expand log_{10}((2x^5)/((7+x)^4)) is log_{10}(2)+5log_{10}(x)-4log_{10}(7+x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand log_{10}((2x^5)/((7+x)^4))

expand

lo g_{10} (\frac{2 x ^{5}}{( 7 + x ) ^{4}})

lo g_{10} (2) + 5 lo g_{10} (x) - 4 lo g_{10} (7 + x)

Solution steps

lo g_{10} (\frac{2 x ^{5}}{( 7 + x ) ^{4}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{2 x ^{5}}{( 7 + x ) ^{4}}) = lo g_{10} (2 x^{5}) - lo g_{10} ((7 + x)^{4})

= lo g_{10} (2 x^{5}) - lo g_{10} ((x + 7)^{4})

Apply log rule:

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

lo g_{10} ((7 + x)^{4}) = 4 lo g_{10} (7 + x)

= lo g_{10} (2 x^{5}) - 4 lo g_{10} (7 + x)

Apply log rule:

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

lo g_{10} (2 x^{5}) = lo g_{10} (2) + lo g_{10} (x^{5})

= lo g_{10} (2) + lo g_{10} (x^{5}) - 4 lo g_{10} (x + 7)

Apply log rule:

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

lo g_{10} (x^{5}) = 5 lo g_{10} (x)

= lo g_{10} (2) + 5 lo g_{10} (x) - 4 lo g_{10} (7 + x)

lo g_{3} (x \cdot sin (x))

ln (4 t)

- 20 lo g_{10} (\frac{2}{5}) + 1.76 + 8 \cdot 6.02

ln (\frac{2.4}{2.08})

lo g_{2} (\frac{7}{11} e^{\frac{15}{4}}) - 10

What is expand log_{10}((2x^5)/((7+x)^4)) ?
The solution to expand log_{10}((2x^5)/((7+x)^4)) is log_{10}(2)+5log_{10}(x)-4log_{10}(7+x)