Question

Решить логарифмическое уравнение log2( +4x+3)=3

Answer 1

Log2(x²+4x+3)=3
x²+4x+3=2³=8
x²+4x+3-8=0
x²+4x-5=0
D=16-4*1*(-5)=16+20=36
x1=(-4+√36)/2=1
x2=(-4-√36)/2=-5

Answer 2

Log(2) (x2+4x+3) = 3
log(2) (x2+4x+3) = log(2) (8)
x2+4x+3=8
x2+4x-5=0
D=16+20 = 36
x(1) = (-4-6)/2 = -5
x(2) =(-4+6)/2 = 1

ОДЗ
х2+4х+3>0
x2+4x+3=0
D=16-12=4
x(1)=(-4+2)/2=-1
x(2) = (-4-2)/2 = -3

график парабола, ветви вверх
///////           //////////
-----o-------o------>x
      -3        -1
ОДЗ:x∈(-∞; -3)U(-1; +∞)

Answer 3

I can help you with your math problem. To solve the logarithmic equation $$\log_2(4x+3)=3$$, you need to apply the following steps:

- Rewrite the equation in exponential form using the definition of logarithm: $$b^{\log_b a}=a$$ - In this case, $$b=2$$ and $$a=4x+3$$, so the equation becomes: $$2^3=4x+3$$ - Simplify the equation by expanding the exponent and subtracting 3 from both sides: $$8=4x+3 \implies 5=4x$$ - Divide both sides by 4 to isolate x: $$x=\frac{5}{4}$$ - Check the solution by plugging it back into the original equation: $$\log_2(4\cdot \frac{5}{4}+3)=\log_2(8)=3$$ - The solution is correct, so the final answer is: $$x=\frac{5}{4}$$

I hope this helps you understand how to solve logarithmic equations. If you have any other questions, feel free to ask me.Ответь+подробно.+Решить+логарифмическое+уравнение+log2(++4x+3)=3