Question

Which equation can you use to evaluate log 1/3^27

Answer 1

To evaluate $\log _{\frac{1}{3}}27$ note that:

• $\dfrac{1}{3}=3^{-1};$
• $27=3^3.$

Use following properties:

1) $\log_ab^k=k\log_ab;$

2) $\log_{a^k}b=\dfrac{1}{k}\log_ab.$

Then

$\log _{\frac{1}{3}}27=\log_{3^{-1}}3^3=3\log_{3^{-1}}3=3\cdot \dfrac{1}{-1}\log_33=-3\log_33.$

Since $\log_aa=1,$ you have

 $\log _{\frac{1}{3}}27=-3.$

Answer 2

Answer:

a on edge

Step-by-step explanation: