Question

Выразите lg A через логарифмы простых чисел. A=720 Как это делать?

Answer 1

Разложим число 720 на простые множители
$720=2^4*5*3^2$
$lg720=lg(2^4*5*3^2)=lg2^4+lg5+lg3^2=4lg2+lg5+2lg3$

Answer 2

Expressing lg(A) in terms of logarithms of prime numbers

To express lg(A) in terms of logarithms of prime numbers, we need to factorize the number A = 720 into its prime factors. Once we have the prime factorization, we can use the properties of logarithms to express lg(A) in terms of logarithms of prime numbers.

Let's factorize A = 720 into its prime factors: A = 2^4 * 3^2 * 5

Now, we can express lg(A) in terms of logarithms of prime numbers using the properties of logarithms: lg(A) = lg(2^4 * 3^2 * 5) = lg(2^4) + lg(3^2) + lg(5) = 4 * lg(2) + 2 * lg(3) + lg(5)

Therefore, lg(A) can be expressed as 4 times the logarithm of 2, plus 2 times the logarithm of 3, plus the logarithm of 5.

Please note that the values of the logarithms of prime numbers can be found in logarithm tables or calculated using a calculator or computer program.

I hope this helps! Let me know if you have any further questions.