How do you solve $e^{3 x} = 5$ $e^(3x)=5$ ?

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Answer 1 · 2016-02-19T07:12:03

Use properties of logarithms to find that $x = \frac{ln (5)}{3}$ $x = ln(5)/3$

We will be using the following properties of logarithms:

Now, using the standard notation of the natural logarithm $ln (x)$ $ln(x)$ to denote ${log}_{e} (x)$ $log_e(x)$ we have:

$e^{3 x} = 5$ $e^(3x) = 5$

$\Rightarrow ln (e^{3 x}) = ln (5)$ $=> ln(e^(3x)) = ln(5)$

$\Rightarrow 3 x ln (e) = ln (5)$ $=> 3xln(e) = ln(5)$

$\Rightarrow 3 x \cdot 1 = ln (5)$ $=> 3x*1 = ln(5)$

$\Rightarrow 3 x = ln (5)$ $=>3x = ln(5)$

$:. x = ln(5)/3$

How do you solve e^(3x)=5e3x=5e^(3x)=5?