What is 2ln(abc)-5ln(ade) ?

The solution to 2ln(abc)-5ln(ade) is ln((b^2c^2)/(de^5a^3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2ln(abc)-5ln(ade)

simplify

2 ln (ab c) - 5 ln (a d e)

ln (\frac{b ^{2} c ^{2}}{d e ^{5} a ^{3}})

Solution steps

2 ln (ab c) - 5 ln (a d e)

Apply log rule:

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

2 ln (ab c) = ln ((ab c)^{2})

= ln ((ab c)^{2}) - 5 ln (d e a)

Apply log rule:

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

5 ln (d e a) = ln ((d e a)^{5})

= ln ((ab c)^{2}) - ln ((d e a)^{5})

Apply log rule:

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

ln ((ab c)^{2}) - ln ((d e a)^{5}) = ln (\frac{( ab c ) ^{2}}{( d e a ) ^{5}})

= ln (\frac{( ab c ) ^{2}}{( a d e ) ^{5}})

Simplify

\frac{( ab c ) ^{2}}{( a d e ) ^{5}} : \frac{b ^{2} c ^{2}}{d e ^{5} a ^{3}}

= ln (\frac{b ^{2} c ^{2}}{d e ^{5} a ^{3}})

ln ∣ 5 ∣ - ln ∣ 4 ∣

6 lo g_{10} (x - 2) - 5 lo g_{10} (x)

ln (40) + 2 ln (\frac{1}{2}) + ln (y)

5 ln (6) - 5 ln (2)

What is 2ln(abc)-5ln(ade) ?
The solution to 2ln(abc)-5ln(ade) is ln((b^2c^2)/(de^5a^3))