Question

Evaluate the following:

`log_(sqrt(3)) 27`

Answer 1

Given: `log_(sqrt(3)) 27`

Step-wise calculation:

Write both base and argument as powers of 3:

`sqrt(3) = 3^(1/2)` and 27 = 3³.

Therefore `log_(sqrt(3))27 = log_(3^(1/2))(3^3)`.

Use the identity

`log_(a^r)(a^s) = s/r`

To get `log_(3^(1/2))(3^3) = 3 ÷ (1/2)`

`log_(3^(1/2))(3^3) = 6`