en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 9ln(a)-6ln(b)

Solution

simplify

9 ln (a) - 6 ln (b)

Solution

ln (\frac{a ^{9}}{b ^{6}})

Solution steps

9 ln (a) - 6 ln (b)

Apply log rule:

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

9 ln (a) = ln (a^{9})

= ln (a^{9}) - 6 ln (b)

Apply log rule:

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

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

= ln (a^{9}) - ln (b^{6})

Apply log rule:

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

ln (a^{9}) - ln (b^{6}) = ln (\frac{a ^{9}}{b ^{6}})

= ln (\frac{a ^{9}}{b ^{6}})

Popular Examples

simplify 2log_{10}(2)+2log_{10}(3)simplify

2 lo g_{10} (2) + 2 lo g_{10} (3)

simplify 2ln(x)+5ln(y)-6ln(z)simplify

2 ln (x) + 5 ln (y) - 6 ln (z)

simplify xln(2)+5ln(x-1)-2ln(x+3)simplify

x ln (2) + 5 ln (x - 1) - 2 ln (x + 3)

simplify ln(243/625)simplify

ln (\frac{243}{625})

simplify ln((e^5)/(11))simplify

ln (\frac{e ^{5}}{11})

Frequently Asked Questions (FAQ)

What is 9ln(a)-6ln(b) ?
The solution to 9ln(a)-6ln(b) is ln((a^9)/(b^6))