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-1.07 approx. is the value of x in [tex]e^{3x + 5}[/tex] =6 solved using natural logarithms
What is a natural logarithm?
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.
We have been asked to solve x for [tex]e^{3x + 5}[/tex] =6 using natural logarithms
⇒ [tex]e^{3x + 5}[/tex] =6
⇒ 3x + 5 = ㏑ 6
⇒ 3x = ㏑6 - 5
⇒ x = [tex]\frac{ln6 - 5}{3}[/tex]
⇒ x = -1.07 approx.
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Correct question
Use natural logarithms to solve each equation.
[tex]e^{3x + 5}[/tex] =6
