What is ln(a)-6ln(b)+5ln(c) ?

The solution to ln(a)-6ln(b)+5ln(c) is ln((ac^5)/(b^6))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(a)-6ln(b)+5ln(c)

simplify

ln (a) - 6 ln (b) + 5 ln (c)

ln (\frac{a c ^{5}}{b ^{6}})

Solution steps

ln (a) - 6 ln (b) + 5 ln (c)

Apply log rule:

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

6 ln (b) = ln (b^{6})

= ln (a) - ln (b^{6}) + 5 ln (c)

Apply log rule:

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

ln (a) - ln (b^{6}) = ln (\frac{a}{b ^{6}})

= ln (\frac{a}{b ^{6}}) + 5 ln (c)

Apply log rule:

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

5 ln (c) = ln (c^{5})

= ln (\frac{a}{b ^{6}}) + ln (c^{5})

Apply log rule:

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

ln (\frac{a}{b ^{6}}) + ln (c^{5}) = ln (c^{5} \frac{a}{b ^{6}})

= ln (c^{5} \frac{a}{b ^{6}})

Multiply fractions:

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

= ln (\frac{a c ^{5}}{b ^{6}})

4 lo g_{3} (X) - 2 lo g_{3} (Y)

lo g_{10} (x^{3} - 7 x + 6) - lo g_{10} (x^{2} + x - 6)

ln (2 \cdot 5)

10 lo g_{10} (\frac{108}{10 8 _{0}})

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

What is ln(a)-6ln(b)+5ln(c) ?
The solution to ln(a)-6ln(b)+5ln(c) is ln((ac^5)/(b^6))