What is 2ln(4)+3ln(x)-4ln(y) ?

The solution to 2ln(4)+3ln(x)-4ln(y) is ln((16x^3)/(y^4))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2ln(4)+3ln(x)-4ln(y)

simplify

2 ln (4) + 3 ln (x) - 4 ln (y)

ln (\frac{16 x ^{3}}{y ^{4}})

Solution steps

2 ln (4) + 3 ln (x) - 4 ln (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (4) = ln (4^{2})

= ln (4^{2}) + 3 ln (x) - 4 ln (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (x) = ln (x^{3})

= ln (4^{2}) + ln (x^{3}) - 4 ln (y)

Apply log rule:

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

ln (4^{2}) + ln (x^{3}) = ln (4^{2} x^{3})

= ln (4^{2} x^{3}) - 4 ln (y)

4^{2} = 16

= ln (16 x^{3}) - 4 ln (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 ln (y) = ln (y^{4})

= ln (16 x^{3}) - ln (y^{4})

Apply log rule:

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

ln (16 x^{3}) - ln (y^{4}) = ln (\frac{16 x ^{3}}{y ^{4}})

= ln (\frac{16 x ^{3}}{y ^{4}})

5 lo g_{2} (k) - 8 lo g_{2} (m) + 10 lo g_{2} (n)

3 ln (A) - \frac{1}{2} [ln (B) + 2 ln (C^{2})]

- lo g_{10} (1.2 \cdot 1 0^{- 2})

ln (x) + ln (sin (x))

3 ln (10) - lo g_{10} (5) - lo g_{10} (2)

What is 2ln(4)+3ln(x)-4ln(y) ?
The solution to 2ln(4)+3ln(x)-4ln(y) is ln((16x^3)/(y^4))