[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{8,903 = e^{5x}}}[/tex]
[tex]\huge\textbf{Simplify:}[/tex]
[tex]\mathsf{8,903 = e^{5x}}}[/tex]
[tex]\mathsf{e^{5x} = 8,903}}[/tex]
[tex]\huge\textbf{Solve for the exponent:}[/tex]
[tex]\large\textsf{We get: }\downarrow\\\\\mathsf{2.718282^{5x}=8903}[/tex]
[tex]\huge\textbf{Take the logarithm from both sides:}[/tex]
[tex]\mathsf{log(2.718282^{5x}) = log(8,903x)}[/tex]
[tex]\large\textsf{We get:}\\\\\mathsf{5x \times log(2.718282)=log(8903)}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{5x = \dfrac{log(8903)}{log(2.718282)}}[/tex]
[tex]\large\textsf{We get: }\\\\\mathsf{5x = 9.094143}[/tex]
[tex]\huge\textbf{Divide 5 to both sides:}[/tex]
[tex]\mathsf{\dfrac{5x}{5} = \dfrac{9.094143}{5}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x= \dfrac{9.094143}{5}}[/tex]
[tex]\mathsf{x = 1.818829}[/tex]
[tex]\mathsf{x \approx 2}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x =}\frak{\ 1.818829}}\huge\checkmark[/tex]
[tex]\large\textbf{Or if you're estimating your answer}\downarrow[/tex]
[tex]\huge\boxed{\mathsf{x \approx }\frak{\ 2}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
