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 * log(2.718282)=log(8903)}`

`\huge\textbf{Simplify it:}`

`\mathsf{5x = (log(8903))/(log(2.718282))}`

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

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

`\mathsf{(5x)/(5) = (9.094143)/(5)}`

`\huge\textbf{Simplify it:}`

`\mathsf{x= (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`

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