Question

Log4(x+2)+log4 3=log4 15​

Answer 1

ОДЗ :

x + 2 > 0

x > - 2

$log_{4}(x+2)+log_{4}3=log_{4}15\\\\log_{4}(x+2)=log_{4}15-log_{4}3\\\\log_{4} (x+2)=log_{4}\frac{15}{3}\\\\log_{4}(x+2)=log_{4}5\\\\x+2=5\\\\x=3\\\\Otvet:3$

Answer 2

To solve the equation log4(x + 2) + log4(3) = log4(15), you can use the properties of logarithms. First, combine the two logarithms on the left side of the equation using the product rule of logarithms, which states that log_a(b) + log_a(c) = log_a(b * c):

log4(x + 2) + log4(3) = log4(15)

log4((x + 2) * 3) = log4(15)

Now that the equation is in a simpler form, you can set the expressions inside the logarithms equal to each other:

(x + 2) * 3 = 15

Now, simplify and solve for x:

3(x + 2) = 15

3x + 6 = 15

Subtract 6 from both sides:

3x = 15 - 6

3x = 9

Now, divide both sides by 3 to solve for x:

x = 9 / 3

x = 3

So, the solution to the equation is x = 3.