Answer :
To solve the problem [tex]\(\log_e 51.7 = x\)[/tex], you need to find the natural logarithm of 51.7. Here is a step-by-step explanation:
1. Understand the Notation: The expression [tex]\(\log_e\)[/tex] is another way to represent the natural logarithm, often written as [tex]\(\ln\)[/tex]. So, [tex]\(\log_e 51.7\)[/tex] is the same as [tex]\(\ln 51.7\)[/tex].
2. Calculating Natural Logarithm: The natural logarithm function gives the power to which the number [tex]\(e\)[/tex] (approximately 2.71828) must be raised to get the number in question, which is 51.7 in this case.
3. Finding the Value: When you calculate [tex]\(\ln 51.7\)[/tex], you obtain a value which tells you how many times you multiply [tex]\(e\)[/tex] by itself to get 51.7.
The calculated value for [tex]\(\log_e 51.7\)[/tex] is approximately 3.9454577815143836. Thus, the solution to the equation [tex]\(\log_e 51.7 = x\)[/tex] is:
[tex]\[ x \approx 3.9454577815143836 \][/tex]
This result represents the power you raise [tex]\(e\)[/tex] to in order to achieve the number 51.7.
1. Understand the Notation: The expression [tex]\(\log_e\)[/tex] is another way to represent the natural logarithm, often written as [tex]\(\ln\)[/tex]. So, [tex]\(\log_e 51.7\)[/tex] is the same as [tex]\(\ln 51.7\)[/tex].
2. Calculating Natural Logarithm: The natural logarithm function gives the power to which the number [tex]\(e\)[/tex] (approximately 2.71828) must be raised to get the number in question, which is 51.7 in this case.
3. Finding the Value: When you calculate [tex]\(\ln 51.7\)[/tex], you obtain a value which tells you how many times you multiply [tex]\(e\)[/tex] by itself to get 51.7.
The calculated value for [tex]\(\log_e 51.7\)[/tex] is approximately 3.9454577815143836. Thus, the solution to the equation [tex]\(\log_e 51.7 = x\)[/tex] is:
[tex]\[ x \approx 3.9454577815143836 \][/tex]
This result represents the power you raise [tex]\(e\)[/tex] to in order to achieve the number 51.7.
