2.4012 is the value of x after solving equation = 30 using natural logarithms
We have been asked to solve = 30 using natural logarithms
⇒ = 30
⇒ x + 1 = ㏑ 30
⇒ x = ㏑ 30 - 1
≈ 2.4012
<h3>What is a natural logarithm?</h3>A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.
The power to which e would need to be raised in order to equal x is the natural logarithm of x.
For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.
Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.
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<h3>Correct Question</h3>Use natural logarithms to solve each equation.
= 30
Solution:
Given:
The value of a car after t - years will depreciate.
Hence, the equation given represents the value after depreciation over t-years.
To get the rate, we compare the equation with the depreciation formula.
Hence,
Therefore, the value of this car is decreasing at a rate of 6%. The purchase price of the car was $16,300.