Answer:
[tex] 2 \log_8 8 [/tex]
Step-by-step explanation:
[tex] 3 \log_8 8 - 2 \log_8 4 + \log_8 2 = [/tex]
[tex] = 3 \log_8 8 - 2 \log_8 4 + \log_8 2 [/tex]
[tex] = 3 \log_8 8 - 2 \log_8 8^\frac{2}{3} + \log_8 8^\frac{1}{3} [/tex]
[tex] = 3 \log_8 8 - 2 \times \dfrac{2}{3} \log_8 8 + \dfrac{1}{3} \log_8 8 [/tex]
[tex] = 3 \log_8 8 - \dfrac{4}{3} \log_8 8 + \dfrac{1}{3} \log_8 8 [/tex]
[tex] = 2 \log_8 8 [/tex]
Which equals simply 2 since log base 8 of 8 is 1.
