Question

Log (8x-5) - найти область определения 2. Сравните : ln 14 и ln 28; Log 0,5 7 и log 0,5 16 5 Срочно надо, помогите!

Answer 1

8x-5>0  8x>5  x>5/8 x∈(5/8. ∞)-область определения
 ln 14<ln28    log0.5   7 >log0.5 16 (функция убывающая)

Answer 2

Finding the Domain of Logarithmic Function

To find the domain of the function log(8x-5), we need to consider the argument of the logarithm. The argument of a logarithm must be greater than 0. Therefore, we set the argument greater than 0 and solve for x.

The argument of the logarithm is (8x-5), so we have: 8x - 5 > 0

Solving for x: 8x > 5 x > 5/8

So, the domain of the function log(8x-5) is x > 5/8.

Comparing Natural Logarithms and Logarithms

1. ln 14 and ln 28: - The natural logarithm of a number is the logarithm to the base e (Euler's number, approximately 2.71828). - ln 14 ≈ 2.639 and ln 28 ≈ 3.332. - Therefore, ln 28 is greater than ln 14.

2. log_0.5 7 and log_0.5 16.5: - The base of the logarithm is 0.5. - log_0.5 7 ≈ -2.807 and log_0.5 16.5 ≈ -4.087. - Therefore, log_0.5 7 is greater than log_0.5 16.5.

I hope this helps! If you have any more questions or need further assistance, feel free to ask.