Thursday, 14 April 2011
Hello everyone, today we learned how to solve exponential equations and logarithmic Functions. First I will start with the lesson on exponential equations.
When solving these types of equations you will first have to make the bases the same and then solve for x from the powers on either side. To make the bases equal each other, first you will look to see which one is simple and then use the base that looks like it could be broken up. When you've broken it up to have the same base as the other side, then you work with the powers and solve for x. This is where your power laws come into play. When you multiply by the same base you add the exponents. And when the bases are the same you make your exponents equal and solve.
Logarithmic Functions: The logarithmic function is the inverse of the exponential function. What you need to know is that you can write exponential statements into equivalent logarithmic form or approach it backwards and write logarithmic statements into equivalent exponential form. An example of an exponential statement is y=4 to the power of x. the Y is your power, the 4 is your base, and the x is your exponent. A good way to remember your power is to know that it is the value on the opposite side of the base and exponent. Now to change into log form, you write down your exponent first then lay down an equal sign, then write log and beside it your base (as a subscript) and your power comes last. So the best way to attack this is to figure out first, which is your exponent, power, and base, in the equation given, and then follow the order: ( exponent; equal sign; log; base(Subscript); and lastly, the power).If you are given the problem in log statement and asked to put it into exponential form, first off, figure out your base, power, and exponent. Then you write down your base, and your exponent as a superscript, an equal sign, and then your power. Another thing to note is that, if you're given a log form that isn't equal to anything, make it equal to something like a variable (X or Y). Then identify your base, power, and exponent, and then write down your base and then your exponent as a superscript, and make it equal to your power. But since your exponet in this case will be equal to whatever variable you choose, you have to figure out what value you can put in place for it, that will equal your power, and then you will write it out as a logarithmic statement. Hopefully this helps you to have a better understanding of exponential equations and logarithmic functions.
When solving these types of equations you will first have to make the bases the same and then solve for x from the powers on either side. To make the bases equal each other, first you will look to see which one is simple and then use the base that looks like it could be broken up. When you've broken it up to have the same base as the other side, then you work with the powers and solve for x. This is where your power laws come into play. When you multiply by the same base you add the exponents. And when the bases are the same you make your exponents equal and solve.
Logarithmic Functions: The logarithmic function is the inverse of the exponential function. What you need to know is that you can write exponential statements into equivalent logarithmic form or approach it backwards and write logarithmic statements into equivalent exponential form. An example of an exponential statement is y=4 to the power of x. the Y is your power, the 4 is your base, and the x is your exponent. A good way to remember your power is to know that it is the value on the opposite side of the base and exponent. Now to change into log form, you write down your exponent first then lay down an equal sign, then write log and beside it your base (as a subscript) and your power comes last. So the best way to attack this is to figure out first, which is your exponent, power, and base, in the equation given, and then follow the order: ( exponent; equal sign; log; base(Subscript); and lastly, the power).If you are given the problem in log statement and asked to put it into exponential form, first off, figure out your base, power, and exponent. Then you write down your base, and your exponent as a superscript, an equal sign, and then your power. Another thing to note is that, if you're given a log form that isn't equal to anything, make it equal to something like a variable (X or Y). Then identify your base, power, and exponent, and then write down your base and then your exponent as a superscript, and make it equal to your power. But since your exponet in this case will be equal to whatever variable you choose, you have to figure out what value you can put in place for it, that will equal your power, and then you will write it out as a logarithmic statement. Hopefully this helps you to have a better understanding of exponential equations and logarithmic functions.
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