(Need asap)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

8. In(6x-5)=3

Respuesta :

msm555

Answer:

x ≈ 4.18092

Step-by-step explanation:

Given the equation [tex] \ln(6x-5) = 3 [/tex], to solve for [tex] x [/tex], we'll use the definition/properties of the natural logarithm:

[tex] \ln(6x-5) = 3 [/tex]

This equation implies that [tex] e^3 = 6x - 5 [/tex], where [tex] e [/tex] is the base of the natural logarithm. The formula used here is the exponential form of logarithms.

Now, we can solve for [tex] x [/tex] as follows:

[tex] e^3 = 6x - 5 [/tex]

Add 5 to both sides:

[tex] e^3 + 5 = 6x - 5 + 5[/tex]

[tex] 6x = e^3 + 5 [/tex]

Divide both sides by 6:

[tex] \dfrac{6x }{6}= \dfrac{e^3 + 5}{6} [/tex]

[tex] x = \dfrac{e^3 + 5}{6} [/tex]

[tex] x \approx 4.1809228205312 [/tex]

[tex] x \approx 4.18092 \textsf{(in 5 d.p.)}[/tex]

Therefore, x ≈ 4.18092

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