Question

. Approximate each of the following logarithms to four decimal places. Use the LOG key on your calculator rather than logarithm tables, first changing the base of the logarithm to 10 if necessary.

log2(3^2)

Answer 1

`log_2(6)=2.584`

Explanation:

Here the logarithm has base 2

`log_2(3^2)=log_2(6)`

Let

`log_2(6)=x`

`log_ya=x\\\Rightarrow y^x=a`

`\\\Rightarrow 2^x=6`

Now, take logarithm to the base 10

`log 2^x=log6\\\Rightarrow xlog2=log6\\\Rightarrow x=(log6)/(log2)\\\Rightarrow x=2.584`

So,
`log_2(6)=2.584`