Question

Log3 (5x+3) = log3(7x+5)

Answer 1

Ответ:

x∈∅

Пошаговое объяснение:

$log_3 (5x+3)=log_3(7x+5)\\ \\1) 5x+3>0; 5x>-3; x>-0,6\\\\2) 7x+5>0; 7x>-5; x>-\frac{5}{7} ; \\\\ x> -0,6\\\\\\5x+3=7x+5\\2x= -2\\x=-1 (x>-0,6)\\x\neq -1$

x∈∅

Answer 2

To solve the equation $\log_3(5x+3) = \log_3(7x+5)$, we can use the properties of logarithms. One key property is that if $\log_a(b) = \log_a(c)$, then $b = c$.

In this case, both sides of the equation have the same base ($3$), so we can apply the property mentioned above:

$\log_3(5x+3) = \log_3(7x+5)$

Since the bases are the same, we can set the arguments equal to each other:

$5x + 3 = 7x + 5$

Now, let's solve for $x$:

Subtract $5x$ from both sides:

$3 = 2x + 5$

Subtract $5$ from both sides:

$-2 = 2x$

Divide both sides by $2$:

$x = -1$

So, the solution to the equation $\log_3(5x+3) = \log_3(7x+5)$ is $x = -1$.