Question

log25-log10+log16-log1
5 5 5 5

Answer 1

Explicație pas cu pas:

$log_{5}(25) - log_{5}(10) + log_{5}(16) - log_{5}(1) = \\ = log_{5}( \frac{25 \cdot 16}{10 \cdot 1} ) = log_{5}(5 \cdot {2}^{3} ) \\ = log_{5}(5) + log_{5}( {2}^{3} ) = 1 + 3log_{5}(2)$

Answer 2

Răspuns:

Explicație pas cu pas:

$log_{5}(25) - log_{5}(10) + log_{5}(16) - log_{5}(1)$

$= log_{5}\Big( \frac{25 \times 16}{10 \times 1} \Big)$

$= log_{5}\Big( \frac{400}{10} \Big)$

$= log_{5}(40)$

$= log_{5}(5 \times 8)$

$= log_{5}(5) + log_{5}(8)$

$= 1 + log_{5}( {2}^{3} ) =\boxed{ 1 + 3 log_{5}(2)}$