What is ln(2x)+2ln(y)-5ln(z) ?

The solution to ln(2x)+2ln(y)-5ln(z) is ln((2xy^2)/(z^5))

Popular >

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

simplify

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

ln (\frac{2 x y ^{2}}{z ^{5}})

Solution steps

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

Apply log rule:

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

2 ln (y) = ln (y^{2})

= ln (2 x) + ln (y^{2}) - 5 ln (z)

Apply log rule:

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

ln (2 x) + ln (y^{2}) = ln (2 x y^{2})

= ln (2 x y^{2}) - 5 ln (z)

Apply log rule:

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

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

= ln (2 x y^{2}) - ln (z^{5})

Apply log rule:

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

ln (2 x y^{2}) - ln (z^{5}) = ln (\frac{2 x y ^{2}}{z ^{5}})

= ln (\frac{2 x y ^{2}}{z ^{5}})

3 lo g_{10} (x) - lo g_{10} (y)

lo g_{3} ((u^{2} v)^{6})

lo g_{10} (21) - lo g_{10} (7)

2 (ln (x) - ln (y)) + \frac{1}{2} ln (z)

4 lo g_{2} (11) - 6 lo g_{2} (6)

What is ln(2x)+2ln(y)-5ln(z) ?
The solution to ln(2x)+2ln(y)-5ln(z) is ln((2xy^2)/(z^5))