Question

Solving Exponential and Logarithmic Equation In exercise,solve for x or t.See example 5 and 6.

Answer 1

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

⇒ $e^{(2x-1)} =\frac{6}{4}$

or

⇒ $e^{(2x-1)} =\frac{3}{2}$

now,

taking natural log both sides, we get

⇒ 2x - 1 = $\ln(\frac{3}{2})$

also,

we know

⇒ $\log(\frac{A}{B}) = \log(A)+\log(B)$

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