Question

Log11(7-5x)=log11(3+x)+1 решить логарифмическое уравнение

Answer 1

Решение
Log₁₁(7-5x) = log₁₁(3+x) + 1
Log₁₁(7-5x) = log₁₁(3+x) + log₁₁ 11
Log₁₁(7-5x) = log₁₁(3+x) * 11
7 - 5x = (3+x) * 11
7 - 5x = 33 + 11x
11x + 5x = 7 - 33
16x = - 26
x = - 26/16
x = - 13/8
x = - 1,625

Answer 2

I can help you solve logarithmic equations. Here is the detailed solution for your query:

$$\log_{11}(7-5x)=\log_{11}(3+x)+1$$

Using the property of logarithms, we can write the equation as:

$$\log_{11}(7-5x)-\log_{11}(3+x)=1$$

$$\log_{11}\left(\frac{7-5x}{3+x}\right)=1$$

Using the definition of logarithms, we can write the equation as:

$$\frac{7-5x}{3+x}=11^1$$

$$\frac{7-5x}{3+x}=11$$

Cross-multiplying, we get:

$$7-5x=33+11x$$

Solving for x, we get:

$$-16x=26$$

$$x=-\frac{13}{8}$$

Therefore, the solution is $$x=-\frac{13}{8}$$.

I hope this helps. If you have any other questions, feel free to ask me.Ответь+подробно.+Log11(7-5x)=log11(3+x)+1+решить+логарифмическое+уравнение