What is ln(a)-3ln(b)+4ln(c) ?

The solution to ln(a)-3ln(b)+4ln(c) is ln((ac^4)/(b^3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(a)-3ln(b)+4ln(c)

simplify

ln (a) - 3 ln (b) + 4 ln (c)

ln (\frac{a c ^{4}}{b ^{3}})

Solution steps

ln (a) - 3 ln (b) + 4 ln (c)

Apply log rule:

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

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

= ln (a) - ln (b^{3}) + 4 ln (c)

Apply log rule:

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

ln (a) - ln (b^{3}) = ln (\frac{a}{b ^{3}})

= ln (\frac{a}{b ^{3}}) + 4 ln (c)

Apply log rule:

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

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

= ln (\frac{a}{b ^{3}}) + ln (c^{4})

Apply log rule:

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

ln (\frac{a}{b ^{3}}) + ln (c^{4}) = ln (c^{4} \frac{a}{b ^{3}})

= ln (c^{4} \frac{a}{b ^{3}})

Multiply fractions:

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

= ln (\frac{a c ^{4}}{b ^{3}})

lo g_{9} ((z x y)^{3})

2 lo g_{\frac{8}{5}} (5)

- lo g_{10} (1.3 \cdot 1 0^{- 10})

ln (5) - 2 (ln (4) + ln (32))

2 ln (8) - 2 ln (6)

What is ln(a)-3ln(b)+4ln(c) ?
The solution to ln(a)-3ln(b)+4ln(c) is ln((ac^4)/(b^3))