vereinfachen-2/3 log_{3}(3m^2)+1/2 log_{3}(9m^2)

Lösung

vereinfachen

- \frac{2}{3} lo g_{3} (3 m^{2}) + \frac{1}{2} lo g_{3} (9 m^{2})

lo g_{3} (\frac{3 3}{3 m})

Schritte zur Lösung

- \frac{2}{3} lo g_{3} (3 m^{2}) + \frac{1}{2} lo g_{3} (9 m^{2})

- \frac{2}{3} lo g_{3} (3 m^{2}) = - lo g_{3} ((3 m^{2})^{\frac{2}{3}})

\frac{1}{2} lo g_{3} (9 m^{2}) = lo g_{3} ((9 m^{2})^{\frac{1}{2}})

= - lo g_{3} ((3 m^{2})^{\frac{2}{3}}) + lo g_{3} ((9 m^{2})^{\frac{1}{2}})

Wende die log Regel an:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{3} ((9 m^{2})^{\frac{1}{2}}) - lo g_{3} ((3 m^{2})^{\frac{2}{3}}) = lo g_{3} \frac{( 9 m ^{2} ) ^{\frac{1}{2}}}{( 3 m ^{2} ) ^{\frac{2}{3}}}

= lo g_{3} \frac{( 9 m ^{2} ) ^{\frac{1}{2}}}{( 3 m ^{2} ) ^{\frac{2}{3}}}

Streiche

\frac{( 9 m ^{2} ) ^{\frac{1}{2}}}{( 3 m ^{2} ) ^{\frac{2}{3}}} : \frac{3 ^{\frac{1}{3}}}{m ^{\frac{1}{3}}}

= lo g_{3} (\frac{3 ^{\frac{1}{3}}}{m ^{\frac{1}{3}}})

Wende Exponentenregel an:

a^{\frac{1}{n}} = n a

3^{\frac{1}{3}} = 33

= lo g_{3} (\frac{3 3}{3 m})

Wende Exponentenregel an:

a^{\frac{1}{n}} = n a

m^{\frac{1}{3}} = 3 m

= lo g_{3} (\frac{3 3}{3 m})

s im pl i f y 5 lo g_{10} (k) - lo g_{10} (q)

s im pl i f y lo g_{10} (\frac{a ^{5} b ^{7}}{c ^{2}})

s im pl i f y ln (x^{5} - 1) - ln (x^{3} - 1)

s im pl i f y 3 lo g_{10} (x + 1) + lo g_{10} (y) - 2 lo g_{10} (x)

s im pl i f y 2 lo g_{10} (x) - lo g_{10} (\frac{1}{x}) - lo g_{10} (y)