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vereinfachen 2log_{10}(b)-1/2 (log_{10}(c)+4log_{10}(d))+5log_{10}(h)

Lösung

vereinfachen

2 lo g_{10} (b) - \frac{1}{2} (lo g_{10} (c) + 4 lo g_{10} (d)) + 5 lo g_{10} (h)

lo g_{10} (\frac{b ^{2} c h ^{5}}{c d ^{2}})

Schritte zur Lösung

2 lo g_{10} (b) - \frac{1}{2} (lo g_{10} (c) + 4 lo g_{10} (d)) + 5 lo g_{10} (h)

Wende die log Regel an:

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

2 lo g_{10} (b) = lo g_{10} (b^{2})

= lo g_{10} (b^{2}) - \frac{1}{2} (lo g_{10} (c) + 4 lo g_{10} (d)) + 5 lo g_{10} (h)

Wende die log Regel an:

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

5 lo g_{10} (h) = lo g_{10} (h^{5})

= lo g_{10} (b^{2}) - \frac{1}{2} (lo g_{10} (c) + 4 lo g_{10} (d)) + lo g_{10} (h^{5})

Wende die log Regel an:

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

lo g_{10} (b^{2}) + lo g_{10} (h^{5}) = lo g_{10} (b^{2} h^{5})

= lo g_{10} (b^{2} h^{5}) - \frac{1}{2} (lo g_{10} (c) + 4 lo g_{10} (d))

Wende die log Regel an:

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

4 lo g_{10} (d) = lo g_{10} (d^{4})

= lo g_{10} (b^{2} h^{5}) - \frac{1}{2} (lo g_{10} (c) + lo g_{10} (d^{4}))

Wende die log Regel an:

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

lo g_{10} (c) + lo g_{10} (d^{4}) = lo g_{10} (c d^{4})

= lo g_{10} (b^{2} h^{5}) - \frac{1}{2} lo g_{10} (c d^{4})

Wende die log Regel an:

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

\frac{1}{2} lo g_{10} (c d^{4}) = lo g_{10} ((c d^{4})^{\frac{1}{2}})

= lo g_{10} (b^{2} h^{5}) - lo g_{10} ((c d^{4})^{\frac{1}{2}})

Wende die log Regel an:

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

lo g_{10} (b^{2} h^{5}) - lo g_{10} ((c d^{4})^{\frac{1}{2}}) = lo g_{10} (\frac{b ^{2} h ^{5}}{( c d ^{4} ) ^{\frac{1}{2}}})

= lo g_{10} (\frac{b ^{2} h ^{5}}{( c d ^{4} ) ^{\frac{1}{2}}})

Vereinfache

\frac{b ^{2} h ^{5}}{( c d ^{4} ) ^{\frac{1}{2}}} : \frac{b ^{2} c h ^{5}}{c d ^{2}}

= lo g_{10} (\frac{b ^{2} c h ^{5}}{c d ^{2}})

s im pl i f y 3 ln (10) - 4 ln (2) - ln (5)

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e x p an d ln (\frac{1 0 ^{- 4} x ^{- 2}}{x ^{5}})

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