Question

Log5(3x-4)=log5(12-5x)

Answer 1

Т.к. основания логарифмов равны, значит равны их подлогарифмические выражения:
$3x-4=12-5x$
$3x+5x=12+4$
$8x=16$
$x=2$ - удовлетворяет условию ОДЗ

ОДЗ:
$\left \{ {{3x-4\ \textgreater \ 0} \atop {12-5x\ \textgreater \ 0}} \right.$

$\left \{ {{x\ \textgreater \ 1 \frac{1}{3} } \atop {x\ \textless \ 2.4 }} \right.$

Ответ: х=2

Answer 2

To solve the equation log₅(3x - 4) = log₅(12 - 5x), we can use the property of logarithms that states if logₐ(x) = logₐ(y), then x = y.

Therefore, we have 3x - 4 = 12 - 5x.

Now, let's solve for x.

First, we can simplify the equation by adding 5x to both sides and adding 4 to both sides:

3x + 5x = 12 + 4,

8x = 16.

Dividing both sides by 8, we get:

x = 2.

So the solution to the equation is x = 2.