Question

Log3(x+2)+1=log3(x+4)

Answer 1

Ответ:

$x=-1$

Пошаговое объяснение:

$\log_3(x+2)+1=\log_3(x+4)\\\log_3(x+2)+\log_33=\log_3(x+4)$

По формуле $\log_ab+\log_zc=\log_a(bc)$

$\log_3(3(x+2))=\log_3(x+4)\\\log_3(3x+6)=\log_3(x+4)\\3x+6=x+4\\2x=4-6\\2x=-2\\x=-1$

Answer 2

To solve the equation $\log_3(x+2)+1=\log_3(x+4)$, we can use logarithmic properties to simplify and solve for $x$. Let's go step by step:

1. Start with the equation: $\log_3(x+2) + 1 = \log_3(x+4)$

2. Subtract $\log_3(x+2)$ from both sides of the equation: $1 = \log_3(x+4) - \log_3(x+2)$

3. Apply the logarithmic property $\log_a(b) - \log_a(c) = \log_a\left(\frac{b}{c}\right)$: $1 = \log_3\left(\frac{x+4}{x+2}\right)$

4. Convert the equation to exponential form: $3^1 = \frac{x+4}{x+2}$

5. Simplify the left side: $3 = \frac{x+4}{x+2}$

6. Cross-multiply: $3(x+2) = x+4$

7. Distribute on the left side: $3x + 6 = x + 4$

8. Subtract $x$ from both sides: $2x + 6 = 4$

9. Subtract 6 from both sides: $2x = -2$

10. Divide by 2: $x = -1$

So, the solution to the equation is $x = -1$. You can plug this value back into the original equation to confirm that it satisfies the equation.