Question

Let x=log 2 and y=log 3

1) log 27

Answer 1

It says express in terms of x and or y

Answer 2

so your log is the decadic logarithm? the base is 10?

Answer 3

I'm late, but I wanna step through this problem with properties of logs.

\[
\begin{split}

\log(27) &= \log(3\times 9) &(1)\\
&= \log(3\times 3 \times 3) &(2)\\
&= \log(3) + \log(3) + \log(3)& (3)\\
&= y + y + y & (4)\\
&=3y &(5)

\end{split}
\]The transition from step \((2)\) to step \((3)\) is just using the logarithmic identity: \[
\log(a\times b) = \log(a) + \log(b)
\]

Answer 4

Other logarithmic properties that is it good to know: \[
\log(a \times b) = \log (a) +\log(b) \\
\log(a \div b) = \log (a) -\log(b) \\
\log(a^b) = b\log (a) \\
\log(\sqrt[b]{a}) = \frac{1}{b}\log (a) \\
\log(1/a) = -\log (a) \\
\log_b(b) = 1\\
\log_b(1) = 0
\]