Question

Log1/3 (27) Log10 (1/10) Log5 (1/125) Log10 100√1000 Вычислить логарифмы С пояснениям

Answer 1

Ответ:

-3

-1

-3

Объяснение:

когда переводишь из дроби в число и наоборот надо брать отрицательную степень, например 3 в степени -1 равно 1/3

это объясняется свойством степеней

в последнем логарифме сначала надо разобраться с корнем, но ты, видимо, забыл или наоборот прибавил лишний ноль

короче решаешь корень, умножаешь его на 100 и ответ будет равен количеству нулей из предыдущего действия

Answer 2

To compute the given logarithms, let's break them down step-by-step and use the properties of logarithms:

1. Log base 1/3 of 27: We want to find the exponent to which 1/3 must be raised to get 27. In other words, we are looking for the solution to the equation (1/3)^x = 27. Rewrite 27 as a power of 1/3: 27 = (1/3)^3 So, x = 3.

   Therefore, log base 1/3 of 27 is equal to 3: log1/3(27) = 3.

2. Log base 10 of 1/10: We want to find the exponent to which 10 must be raised to get 1/10. In other words, we are looking for the solution to the equation 10^x = 1/10. Rewrite 1/10 as a power of 10: 1/10 = 10^(-1) So, x = -1.

   Therefore, log base 10 of 1/10 is equal to -1: log10(1/10) = -1.

3. Log base 5 of 1/125: We want to find the exponent to which 5 must be raised to get 1/125. In other words, we are looking for the solution to the equation 5^x = 1/125. Rewrite 1/125 as a power of 5: 1/125 = 5^(-3) So, x = -3.

   Therefore, log base 5 of 1/125 is equal to -3: log5(1/125) = -3.

4. Log base 10 of 100√1000: We want to find the exponent to which 10 must be raised to get 100√1000. In other words, we are looking for the solution to the equation 10^x = 100√1000. Simplify 100√1000 first: 100√1000 = 100 * √(1000) = 100 * 10 = 1000.

   Now, the equation becomes: 10^x = 1000. Rewrite 1000 as a power of 10: 1000 = 10^3 So, x = 3.

   Therefore, log base 10 of 100√1000 is equal to 3: log10(100√1000) = 3.

To summarize:

• log1/3(27) = 3
• log10(1/10) = -1
• log5(1/125) = -3
• log10(100√1000) = 3