Question

18. Calculate the following logarithms.
c. log9(3)

Answer 1

`\log_(9)(3) = (1)/(2)`

Explanation:

To solve logarithms, we have to consider the following:

`\log_(a)(b) = c` means that
`a^(c) = b`.

So, for example:

`\log_(10)(100) = 2` means that
`10^(2) = 100`.

So

`\log_(9)(3) = x`

`9^(x) = 3^(1)`

9 is 3*3. So

`3^(2x) = 3^(1)`

`2x = 1`

`x = (1)/(2)`

So

`\log_(9)(3) = (1)/(2)`