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

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

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{y ^{4} z ^{0.5}}{x ^{3}})

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

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

Apply log rule:

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

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

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

Multiply fractions:

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

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

ln (- 2 e^{- 2 x})

\frac{1}{3} ln (11) - ln (2)

ln (35) + ln (\frac{1}{7})

ln (\frac{16}{9})

ln (11) - ln (0.002)

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