Oblicz. `log_(2) 5 + log_(4) 18`
`log_(2) 15 + 1/2`
`log_(2) 15`
`log_(1/2) 15 + 2`
`log_(2) 23 + 1/2`
Skorzystaj z własności logarytmów.
`log_(2) 5 + log_(4) 18 =` `= log_(2) 5 + log_(4) (2 cdot 9) =` `= log_(2) 5 + log_(4) 2 + log_(4) 9 =` `= log_(2) 5 + log_(2^2) 2 + log_(2^2) 3^2 =` `= log_(2) 5 + 1/2log_(2) 2 + 1/2log_(2) 3^2 =` `= log_(2) 5 + 1/2log_(2) 2 + 1/2 cdot 2 cdot log_(2) 3 =` `= log_(2) 5 + 1/2+ log_(2) 3 =` `= log_(2) (5 cdot 3) + 1/2 =` `= log_(2) 15 + 1/2`