simplificar 1/2 [6ln(x-3)+ln(x)-2ln(x)]

Solução

simplificar

\frac{1}{2} [6 ln (x - 3) + ln (x) - 2 ln (x)]

\frac{1}{2} ln (\frac{( x - 3 ) ^{6}}{x})

Passos da solução

\frac{1}{2} [6 ln (x - 3) + ln (x) - 2 ln (x)]

Aplicar as propriedades dos logaritmos:

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

6 ln (x - 3) = ln ((x - 3)^{6})

= \frac{1}{2} [ln ((x - 3)^{6}) + ln (x) - 2 ln (x)]

Aplicar as propriedades dos logaritmos:

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

ln ((x - 3)^{6}) + ln (x) = ln (x (x - 3)^{6})

= \frac{1}{2} [ln ((x - 3)^{6} x) - 2 ln (x)]

Aplicar as propriedades dos logaritmos:

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

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

= \frac{1}{2} [ln (x (x - 3)^{6}) - ln (x^{2})]

Aplicar as propriedades dos logaritmos:

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

ln (x (x - 3)^{6}) - ln (x^{2}) = ln (\frac{x ( x - 3 ) ^{6}}{x ^{2}})

= \frac{1}{2} [ln (\frac{x ( x - 3 ) ^{6}}{x ^{2}})]

Eliminar o fator comum:

x

= \frac{1}{2} [ln (\frac{( x - 3 ) ^{6}}{x})]

Remover os parênteses:

(a) = a

= \frac{1}{2} ln (\frac{( x - 3 ) ^{6}}{x})

s im pl i f y lo g_{10} (6) + lo g_{10} (3)

s im pl i f y \frac{1}{2} ln (\frac{1}{2})

s im pl i f y - lo g_{10} (3.8 \cdot 1 0^{- 4})

s im pl i f y 2 lo g_{10} (x) - 3 lo g_{10} (x y) - 4 lo g_{10} (y)

s im pl i f y lo g_{4} (x^{2} - 64) - 6 lo g_{4} (x + 8)