Question

Log6(5х+3) = log6(7х−5)

Answer 1

Ответ:

Пошаговое объяснение:

ОДЗ

5x+3>0   x>-3/5

7x-5>0    х> 5/7  

ОДЗ х> 5/7  

5х+3 = 7х−5

7х-5х=3+5

2х=8

х=8/2

x=4

Answer 2

To solve the equation log6(5x + 3) = log6(7x - 5), we can use the property of logarithms that states:

log_b(a) = log_c(a) if and only if a = c

In this case, the bases of both logarithms are the same (base 6), so we can equate the expressions inside the logarithms:

5x + 3 = 7x - 5

Now, let's solve for x:

Subtract 5x from both sides:

5x + 3 - 5x = 7x - 5 - 5x

3 = 2x - 5

Add 5 to both sides:

3 + 5 = 2x - 5 + 5

8 = 2x

Divide both sides by 2:

8/2 = 2x/2

4 = x

So the solution to the equation is x = 4. You can verify this by substituting x = 4 back into the original equation to ensure both sides are equal.