Question

Срочно!Вычислить: log5 12, если log5 2 = d и log5 3= t. ​

Answer 1

Ответ:

$2d+t$

Объяснение:

$log_am^n=n*log_am$

$log_a(mn)=log_am+log_an\\\\log_52=d,\;\;\;\;log_53=t\\\\log_512=log_5(2^2*3)=log_52^2+log_53=2log_52+log_53=2d+t$

Answer 2

To find the value of log base 5 of 12, we can use the properties of logarithms. Specifically, we can express log base 12 in terms of d and t using the following rules:

1. log_a (b) + log_a (c) = log_a (b * c) (Logarithm multiplication rule)
2. log_a (b) - log_a (c) = log_a (b / c) (Logarithm division rule)

We are given that: log5 2 = d log5 3 = t

Now, we need to find log5 12. We can express 12 as a product of numbers whose logarithms we already know:

12 = 2 * 2 * 3

Now, we can use the properties of logarithms:

log5 12 = log5 (2 * 2 * 3)

Since log5 (2 * 2 * 3) is the sum of logarithms, we can use the logarithm multiplication rule:

log5 (2 * 2 * 3) = log5 2 + log5 2 + log5 3

Now, we substitute the given values:

log5 12 = d + d + t

So, the final answer is:

log5 12 = 2d + t