Question

Log_5(x+10)=Log_5(2*x+5)

Answer 1

ОДЗ: $\displaystyle \left \{ {{x+10>0} \atop {2x+5>0}} \right.~~~\Rightarrow~~\left \{ {{x>-10} \atop {x>-2.5}} \right.~~\Rightarrow~~ x>-2.5$

$\log_5(x+10)=\log_5(2x+5)\\ \\ x+10=2x+5\\ \\ x-2x=5-10\\ \\ -x=-5\\ \\ x=5$

Ответ: 5.

Answer 2

To solve the equation Log_5(x+10) = Log_5(2*x+5), we can use the properties of logarithms. One of the key properties is that if Log_a(b) = Log_a(c), then b = c.

So, in this case, we can set the expressions inside the logarithms equal to each other:

x + 10 = 2*x + 5

Now, we can solve for x:

Subtract x from both sides:

x + 10 - x = 2*x + 5 - x

10 = x + 5

Subtract 5 from both sides:

10 - 5 = x + 5 - 5

5 = x

So, the solution to the equation is x = 5.