Question

Посчитать log6 2/log6 0.5

Answer 1

$\dfrac{ \log_{6}(2) }{ \log_{6} (0.5) } = \dfrac{ \log_{6}(2) }{ \log_{6} ( {2}^{ - 1} ) } = \dfrac{ \log_{6}(2) }{ - \log_{6} (2) } = - 1$

Answer 2

Ответ:

-1

Пошаговое объяснение:

log6(2)

________

log6(2^-1)

log6(2)

______

-log6(2)

сократим:

получается -1

Answer 3

To calculate the expression log6 2/log6 0.5, we can use the logarithmic property that states: logₐ b / logₐ c = log_c b.

Therefore, we have:

log₆ 2 / log₆ 0.5 = log₀.₅ 2

Now, we need to determine the logarithm base that satisfies log_c b = log₀.₅ 2.

Using the logarithmic change of base formula, we can rewrite log_c b as log b / log c.

log₀.₅ 2 = log 2 / log 0.5

Now, we can calculate the logarithms of 2 and 0.5 in any base, such as the natural logarithm (base e) or the common logarithm (base 10).

Using the common logarithm (base 10) as an example:

log₀.₅ 2 ≈ log 2 / log 0.5 ≈ 0.301 / (-0.301) ≈ -1

Therefore, log₆ 2 / log₆ 0.5 ≈ -1.