Since we have e = 2.718281828459, a becomes 2.718281828459

Take the natural log of both sides

Ln(e^{2q}) = Ln(48)

Use a logarithmic identity

Ln(a^{n}) = n * Ln(a)

Using that identity, we have n = 2q and a = e, so our equation becomes:

2qLn(e) = 3.8712010109079

Given that e = 2.718281828459, we have:

2q * Ln(2.718281828459)

Evaluate outside constant

(2 * 1)q = 3.8712010109079

2q = 3.8712010109079

Divide each side of the equation by 2

2q

2

=

3.8712010109079

2

Final Answer

q = 1.9356005054539

What is the Answer?

q = 1.9356005054539

How does the Logarithms and Natural Logarithms and Eulers Constant (e) Calculator work?

Free Logarithms and Natural Logarithms and Eulers Constant (e) Calculator - This calculator does the following:
* Takes the Natural Log base e of a number x Ln(x) → log_{e}x
* Raises e to a power of y, e^{y}
* Performs the change of base rule on log_{b}(x)
* Solves equations in the form b^{cx} = d where b, c, and d are constants and x is any variable a-z
* Solves equations in the form ce^{dx}=b where b, c, and d are constants, e is Eulers Constant = 2.71828182846, and x is any variable a-z
* Exponential form to logarithmic form for expressions such as 5^{3} = 125 to logarithmic form
* Logarithmic form to exponential form for expressions such as Log_{5}125 = 3

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