Question

Log¹/7(5x-6)=log¹/7(4x)=

Answer 1

ОДЗ :

1) 5x - 6 > 0

5x > 6

x > 1,2

2) 4x > 0

x > 0

Окончательно : x > 1,2

$log_{\frac{1}{7} }(5x-6)=log_{\frac{1}{7}}4x\\\\5x-6=4x\\\\5x-4x=6\\\\x=6$

Ответ : 6

Answer 2

To solve the equation:

log¹/7(5x - 6) = log¹/7(4x)

We need to remember the properties of logarithms. In particular, when two logarithms with the same base are equal, then their arguments (what is inside the logarithm) must be equal as well.

So, in this case, we have:

5x - 6 = 4x

Now, we can solve for x:

Subtract 4x from both sides:

5x - 4x - 6 = 0

x - 6 = 0

Add 6 to both sides:

x = 6

Thus, the solution to the equation is x = 6.