Question

Solve the following 8903=e

Answer 1

$\huge\text{Hey there!}$

$\huge\textbf{Equation:}$

$\mathsf{8,903 = e^{5x}}}$

$\huge\textbf{Simplify:}$

$\mathsf{8,903 = e^{5x}}}$

$\mathsf{e^{5x} = 8,903}}$

$\huge\textbf{Solve for the exponent:}$

$\large\textsf{We get: }\downarrow\\\\\mathsf{2.718282^{5x}=8903}$

$\huge\textbf{Take the logarithm from both sides:}$

$\mathsf{log(2.718282^{5x}) = log(8,903x)}$

$\large\textsf{We get:}\\\\\mathsf{5x \times log(2.718282)=log(8903)}$

$\huge\textbf{Simplify it:}$

$\mathsf{5x = \dfrac{log(8903)}{log(2.718282)}}$

$\large\textsf{We get: }\\\\\mathsf{5x = 9.094143}$

$\huge\textbf{Divide 5 to both sides:}$

$\mathsf{\dfrac{5x}{5} = \dfrac{9.094143}{5}}$

$\huge\textbf{Simplify it:}$

$\mathsf{x= \dfrac{9.094143}{5}}$

$\mathsf{x = 1.818829}$

$\mathsf{x \approx 2}$

$\huge\textbf{Therefore, your answer should be:}$

$\huge\boxed{\mathsf{x =}\frak{\ 1.818829}}\huge\checkmark$

$\large\textbf{Or if you're estimating your answer}\downarrow$

$\huge\boxed{\mathsf{x \approx }\frak{\ 2}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~$\frak{Amphitrite1040:)}$