Answer:
[tex] log_{3}(27 \cdot 81) = 7[/tex]
[tex] log_{3}27 = 3 [/tex]
[tex] log_{3}81 = 4 [/tex]
Step-by-step explanation:
Logarithmic Power rule
[tex] log_{a}b^m= m \cdot log_{a}b [/tex]
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Problem 1
[tex] log_{3}(27\cdot 81) = log_{3}(3^3 \cdot 3^4) [/tex]
[tex] log_{3}(27\cdot 81) = log_{3}3^7 [/tex]
[tex] log_{3}(27\cdot 81) = 7\cdot log_{3}3 [/tex]
[tex] log_{3}(27\cdot 81) = 7\cdot 1 [/tex]
[tex] log_{3}(27\cdot 81) = 7 [/tex]
Problem 2
[tex] log_{3}27 = log_{3}(3^3) [/tex]
[tex] log_{3}27 = 3\cdot log_{3}3 [/tex]
[tex] log_{3}27 = 3\cdot 1 [/tex]
[tex] log_{3}27 = 3 [/tex]
Problem 3
[tex] log_{3}81 = log_{3}(3^4) [/tex]
[tex] log_{3}81 = 4\cdot log_{3}3 [/tex]
[tex] log_{3}81 = 4\cdot 1 [/tex]
[tex] log_{3}81 = 4 [/tex]
