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AlladinOne [14]
3 years ago
11

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

Mathematics
1 answer:
Aloiza [94]3 years ago
3 0

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

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