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