Answer:
0.70275
Step-by-step explanation:
Data provided in the question:
4e²ˣ⁻¹ -1 = 5
now solving for 'x'
⇒ 4e²ˣ⁻¹ = 5 + 1
or
⇒ 4e²ˣ⁻¹ = 6
or
⇒ [tex]e^{(2x-1)} =\frac{6}{4}[/tex]
or
⇒ [tex]e^{(2x-1)} =\frac{3}{2}[/tex]
now,
taking natural log both sides, we get
⇒ 2x - 1 = [tex]\ln(\frac{3}{2})[/tex]
also,
we know
⇒ [tex]\log(\frac{A}{B}) = \log(A)+\log(B)[/tex]
thus,
⇒ 2x - 1 = ln(3) - ln(2)
or
⇒ 2x - 1 = 1.0986 - 0.6931
or
⇒ 2x - 1 = 0.4055
or
⇒ 2x = 0.4055 + 1
or
⇒ 2x = 1.4055
or
⇒ x = 0.70275
