Question

( 3 - log3 8) / (1 + log 3 0.5) =....

Answer 1

Свойства логарифма нужно знать

Answer 2

To solve this expression, we can start by simplifying the logarithmic terms.

Recall the logarithmic property: log_a b = log_c b / log_c a, where "c" can be any positive base, but it needs to be consistent for both the numerator and denominator. In this case, we'll use base 3 since the logarithms are given in base 3.

1. Simplify the numerator:

(3 - log3 8) = 3 - log3 2^3 = 3 - 3 * log3 2 = 3 - 3 * (log3 2 / log3 3) [Using the logarithmic property] = 3 - 3 * (log3 2 / 1) [Since log3 3 = 1]

2. Simplify the denominator:

(1 + log3 0.5) = 1 + log3 (1/2) = 1 - log3 2 = 1 - (log3 2 / log3 3) [Using the logarithmic property] = 1 - (log3 2 / 1) [Since log3 3 = 1]

Now the expression becomes:

(3 - 3 * (log3 2 / 1)) / (1 - (log3 2 / 1))

Since log3 2 is approximately 0.6309, we can now compute the result:

(3 - 3 * 0.6309) / (1 - 0.6309) (3 - 1.8927) / (0.3691) 1.1073 / 0.3691 ≈ 3.0000

So, (3 - log3 8) / (1 + log 3 0.5) is approximately equal to 3.