Esercizio
$\ln\left(x^5\right)-\frac{1}{3}\ln\left(x^{-7}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. Condense the logarithmic expression ln(x^5)-1/3ln(x^(-7)). Applicare la formula: a\ln\left(x\right)=-\ln\left(x^{\left|a\right|}\right), dove a=-\frac{1}{3} e x=x^{-7}. Simplify \sqrt[3]{x^{-7}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals -7 and n equals \frac{1}{3}. Applicare la formula: \ln\left(a\right)-\ln\left(b\right)=\ln\left(\frac{a}{b}\right), dove a=x^5 e b=x^{-\frac{7}{3}}. Applicare la formula: \frac{a^m}{a^n}=a^{\left(m-n\right)}, dove a^n=x^{-\frac{7}{3}}, a^m=x^5, a=x, a^m/a^n=\frac{x^5}{x^{-\frac{7}{3}}}, m=5 e n=-\frac{7}{3}.
Condense the logarithmic expression ln(x^5)-1/3ln(x^(-7))
Risposta finale al problema
$\ln\left(\sqrt[3]{x^{22}}\right)$