Question

Log 1/4 (4x+3)=-1 решите логарифМ, очень срочно, с одз 1/4 - основание

Answer 1

4x + 3 = (1/4) ⁻¹
4x + 3 = 4
4x = 1
x = 1/4

ОДЗ здесь находить не надо, так как логарифмируемое выражение приравнивается к степени, а степень всегда положительна.

Answer 2

 ОДЗ 4x+3>0 => х>-3/4,   -1=log1/4(4x+3)=-log4(4x+3) => 4=4x+3=> x=1/4 Ответ х=1/4  

Answer 3

Solving the Logarithmic Equation

To solve the logarithmic equation log(1/4)(4x+3) = -1 with the base of 1/4, we can use the properties of logarithms to simplify and solve for x.

First, let's rewrite the equation using the property that log(a)b = log(c)b / log(c)a:

log(1/4)(4x+3) = -1

This can be rewritten as:

log(4x+3) / log(1/4) = -1

Now, we can use the fact that log(a)b = c is equivalent to b = a^c to rewrite the equation as an exponential equation:

4x + 3 = (1/4)^(-1)

Simplifying the Exponential Equation

The next step is to simplify (1/4)^(-1):

(1/4)^(-1) = 4

So, the equation becomes:

4x + 3 = 4

Solving for x

Now, we can solve for x:

4x = 4 - 3

4x = 1

x = 1/4

Conclusion

Therefore, the solution to the logarithmic equation log(1/4)(4x+3) = -1 with the base of 1/4 is x = 1/4.