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  • 15-01-2020
  • Mathematics
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Solving Exponential and Logarithmic Equation In exercise,solve for x or t.See example 5 and 6.
4e2x - 1 -1 = 5

Respuesta :

valetta valetta
  • 15-01-2020

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

Answer Link

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