Question

Rewrite log_6[(a/b)^4*c] using the properties of logarithms.

Answer 1

We have the expression:

`\log _6\lbrack((a)/(b))^4\cdot c\rbrack`

And we have to rewrite it using the properties of logarithms.

We will go step by step as:

`\begin{gathered} \log _6\lbrack((a)/(b))^4\cdot c\rbrack \\ \log _6\lbrack((a)/(b))^4\rbrack+\log _6(c) \\ 4\cdot\log _6((a)/(b))+\log _6(c)_{} \\ 4\lbrack\log _6(a)-\log _6(b)\rbrack+\log (c) \\ 4\cdot\log _6(a)-4\cdot\log _6(b)+\log (c) \end{gathered}`

Then we have:

`\log _6\lbrack((a)/(b))^4\cdot c\rbrack=4\cdot\log _6(a)-4\cdot\log _6(b)+\log (c)`

Answer: Option 1

4*log_6(a)-4*log_6(b)+log_6(c)