What is 1+3ln(x)-4ln(y)+0.5ln(z) ?

The solution to 1+3ln(x)-4ln(y)+0.5ln(z) is 1+ln((x^3z^{0.5})/(y^4))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1+3ln(x)-4ln(y)+0.5ln(z)

simplify

1 + 3 ln (x) - 4 ln (y) + 0.5 ln (z)

1 + ln (\frac{x ^{3} z ^{0.5}}{y ^{4}})

Solution steps

1 + 3 ln (x) - 4 ln (y) + 0.5 ln (z)

Apply log rule:

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

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

= 1 + ln (x^{3}) - 4 ln (y) + 0.5 ln (z)

Apply log rule:

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

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

= 1 + ln (x^{3}) - ln (y^{4}) + 0.5 ln (z)

Apply log rule:

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

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

= 1 + ln (\frac{x ^{3}}{y ^{4}}) + 0.5 ln (z)

Apply log rule:

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

0.5 ln (z) = ln (z^{0.5})

= 1 + ln (\frac{x ^{3}}{y ^{4}}) + ln (z^{0.5})

Apply log rule:

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

ln (\frac{x ^{3}}{y ^{4}}) + ln (z^{0.5}) = ln (\frac{x ^{3}}{y ^{4}} z^{0.5})

= 1 + ln (\frac{x ^{3}}{y ^{4}} z^{0.5})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 1 + ln (\frac{x ^{3} z ^{0.5}}{y ^{4}})

ln (ln (x)) - ln (x)

ln (\frac{1}{2.994})

ln (x^{2} + 1) - ln (x^{2} - 4)

ln (\frac{a ^{3}}{( a + 1 ) ^{2}})

ln (v) - ln (20)

What is 1+3ln(x)-4ln(y)+0.5ln(z) ?
The solution to 1+3ln(x)-4ln(y)+0.5ln(z) is 1+ln((x^3z^{0.5})/(y^4))