At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To determine which equation is equivalent to the logarithmic equation
[tex]\[ x = \ln 4 \][/tex]
we need to recall that the natural logarithm function, [tex]\(\ln y\)[/tex], is the power to which the base [tex]\(e\)[/tex] (approximately 2.718) must be raised to yield [tex]\(y\)[/tex]. In other words, the equation
[tex]\[ x = \ln 4 \][/tex]
can be converted to its exponential form.
Given [tex]\(\ln y = x\)[/tex] converts to [tex]\(e^x = y\)[/tex], we can apply this rule to our original equation:
1. Start with the equation:
[tex]\[ x = \ln 4 \][/tex]
2. Recall the definition of the natural logarithm: [tex]\(\ln y = x\)[/tex] means [tex]\(e^x = y\)[/tex].
3. Apply this definition to our equation:
[tex]\[ e^x = 4 \][/tex]
Thus, the equivalent equation to [tex]\( x = \ln 4 \)[/tex] is:
[tex]\[ e^x = 4 \][/tex]
Now let's check the options provided:
A. [tex]\( e^4 = x \)[/tex]
B. [tex]\( e^x = 4 \)[/tex]
C. [tex]\( x^4 = e \)[/tex]
D. [tex]\( x = \log_{10} 4 \)[/tex]
The correct choice, based on our conversion, is:
B. [tex]\( e^x = 4 \)[/tex]
[tex]\[ x = \ln 4 \][/tex]
we need to recall that the natural logarithm function, [tex]\(\ln y\)[/tex], is the power to which the base [tex]\(e\)[/tex] (approximately 2.718) must be raised to yield [tex]\(y\)[/tex]. In other words, the equation
[tex]\[ x = \ln 4 \][/tex]
can be converted to its exponential form.
Given [tex]\(\ln y = x\)[/tex] converts to [tex]\(e^x = y\)[/tex], we can apply this rule to our original equation:
1. Start with the equation:
[tex]\[ x = \ln 4 \][/tex]
2. Recall the definition of the natural logarithm: [tex]\(\ln y = x\)[/tex] means [tex]\(e^x = y\)[/tex].
3. Apply this definition to our equation:
[tex]\[ e^x = 4 \][/tex]
Thus, the equivalent equation to [tex]\( x = \ln 4 \)[/tex] is:
[tex]\[ e^x = 4 \][/tex]
Now let's check the options provided:
A. [tex]\( e^4 = x \)[/tex]
B. [tex]\( e^x = 4 \)[/tex]
C. [tex]\( x^4 = e \)[/tex]
D. [tex]\( x = \log_{10} 4 \)[/tex]
The correct choice, based on our conversion, is:
B. [tex]\( e^x = 4 \)[/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.