What is ln(a^2*e)-ln(1/a)-ln(e^2) ?

The solution to ln(a^2*e)-ln(1/a)-ln(e^2) is ln(ea^3)-2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(a^2*e)-ln(1/a)-ln(e^2)

simplify

ln (a^{2} \cdot e) - ln (\frac{1}{a}) - ln (e^{2})

ln (e a^{3}) - 2

Solution steps

ln (a^{2} e) - ln (\frac{1}{a}) - ln (e^{2})

Apply log rule:

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

ln (e a^{2}) - ln (\frac{1}{a}) = ln (\frac{e a ^{2}}{\frac{1}{a}})

= ln (\frac{e a ^{2}}{\frac{1}{a}}) - ln (e^{2})

Simplify

\frac{a ^{2} e}{\frac{1}{a}} : e a^{3}

= ln (e a^{3}) - ln (e^{2})

ln (e^{2}) = 2

= ln (e a^{3}) - 2

ln (5 e) 4

- lo g_{10} (2.1 \cdot 1 0^{- 6})

3 lo g_{2} (x) - 4 lo g_{2} (y) + \frac{1}{2} lo g_{2} (z)

ln (2 (7) + 1) + 2 ln ((7) - 1)

lo g_{10} (x^{3} + 3 x^{2} - 4 x) - lo g_{10} (x^{2} - 2 x + 1)

What is ln(a^2*e)-ln(1/a)-ln(e^2) ?
The solution to ln(a^2*e)-ln(1/a)-ln(e^2) is ln(ea^3)-2