Question

Lg(x+6)+lg(x+6)=1+lg(6+4)​

Answer 1

Ответ:

x=4

Пошаговое объяснение:

lg(x+6)+lg(x+6)=1+lg(6+4)

lg(x+6)²=lg10+lg10

lg(x+6)²=lg100

(x+6)²=100

x²+12x+36-100=0

x²+12x-64=0

x1=4

x2=-16

Одз:

х+6>0

x>-6

Answer 2

To solve the equation $\log(x+6) + \log(x+6) = 1 + \log(6+4)$, we'll use logarithm properties to simplify and isolate $x$:

First, let's simplify the right-hand side using the properties of logarithms:

$\log(6+4) = \log(10)$ (since $6 + 4 = 10$)

Now, we can rewrite the equation:

$2\log(x+6) = 1 + \log(10)$

Next, we'll use the properties of logarithms to simplify further:

$\log((x+6)^2) = \log(10) + 1$

Now, we can equate the arguments of the logarithms:

$(x+6)^2 = 10e$ (where $e$ is the base of the natural logarithm)

Now, we'll take the square root of both sides:

$x+6 = \sqrt{10e}$ or $x+6 = -\sqrt{10e}$

Now, we'll isolate $x$:

1. $x = \sqrt{10e} - 6$
2. $x = -\sqrt{10e} - 6$

These are the solutions for $x$ in terms of $e$. If you'd like numerical approximations, you'll need to plug in the value of $e$ (approximately 2.71828) and calculate the respective values.