Diketahui log 2 = a dan log 3 = b. Nilai log 15 pangkat 2/3?

→ Materi : Logaritma ←
≡ Diketahui:
[tex]\Leftrightarrow \log 2=a \\ \Leftrightarrow \log 3=b[/tex]

≡ Sifat logaritma yang dipakai:
[tex]\Rightarrow \log \; (\frac{a}{b})=\log a- \log b \\ \Rightarrow \log a^{b}=b \times \log a[/tex]

≡ Penyelesaian:
[tex]\rightarrow \log 15^{\frac{2}{3}} \\ \rightarrow \frac{2}{3} \times \log 15 \\ \rightarrow \frac{2}{3} \times [\log(5 \times 3)] \\ \rightarrow \frac{2}{3} \times (\log 5+ \log 3) \\ \rightarrow \frac{2}{3} \times [\log (\frac{10}{2})+\log 3] \\ \rightarrow \frac{2}{3} \times (\log 10-\log 2+ \log 3) \\ \rightarrow \frac{2}{3} \times (1-a+b) \\ \leadsto \boxed{\frac{2}{3}b-\frac{2}{3}a+\frac{2}{3}}[/tex]