nmomma83
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Solve each equation. Use one of the 4 methods you have practiced the last few days:
1. Write exponents using the same base
2. Take the log of both sides
3. Use properties of logs then write as an exponent
4. Use properties of logs then drop the log on both sides

3. Log(4x-2)=log(-5x+5)

Respuesta :

msm555

Answer:

x ≈ 0.78

Step-by-step explanation:

To solve the equation [tex]\sf \log(4x-2) = \log(-5x+5)[/tex], we can use the logarithmic identity/property which states that if [tex]\sf \log_a(x) = \log_a(y)[/tex], then [tex]\sf x = y[/tex], provided that both [tex]\sf x[/tex] and [tex]\sf y[/tex] are positive.

Given the equation,

[tex]\sf \log(4x-2) = \log(-5x+5)[/tex]

We can apply the mentioned logarithmic rule to conclude that

[tex]\sf 4x - 2 = -5x + 5[/tex]

Here, the rule states that if two logarithmic expressions with the same base are equal, then their arguments must also be equal.

Now, solve for [tex]\sf x[/tex]:

[tex]\sf 4x + 5x = 5 + 2[/tex]

[tex]\sf 9x = 7[/tex]

[tex]\sf x = \dfrac{7}{9}[/tex]

[tex]\sf x \approx 0.7777777777777... [/tex]

[tex]\sf x \approx 0.78 \textsf{(in 2 d.p.)}[/tex]

Therefore, x ≈ 0.78.

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