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Fo: [12 Points]DETAILSPREVIOUS ANSWERSLARCALCET7 1.6.JIT.0MY NOTESASK YOUR TEACHERPRACTICE ANOTHERExpress the equation in logarithmic form_ (a)x =In(7)(b)=yX=eNeed ...

Question

Fo: [12 Points]DETAILSPREVIOUS ANSWERSLARCALCET7 1.6.JIT.0MY NOTESASK YOUR TEACHERPRACTICE ANOTHERExpress the equation in logarithmic form_ (a)x =In(7)(b)=yX=eNeed Help?Read ItSubmit Answer[1/1 Points]DETAILSPREVIOUS ANSWERSLARCALCET7 1.6JJIT_

Fo: [12 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 1.6.JIT.0 MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Express the equation in logarithmic form_ (a) x =In(7) (b) =y X=e Need Help? Read It Submit Answer [1/1 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 1.6JJIT_



Answers

For the following exercises, rewrite each equation in logarithmic form.
$$10^{a}=b$$

So we have an exponential equation here. That equation is 10 to the A is equal to be. We want to convert this to a log rhythmic equation. So the first thing that we want to do is we'll want to identify the base of the exponential function because that will form the base of our logger them as well. So our base here, in our exponential function is just tense. That will also be the base of our log rhythm. But when we're writing any longer, them with the base of 10 were actually working with a common lager of them. So we don't even need to write the 10. It'll just be a log of some number is equal to some number or some variable. The next thing that we're gonna want to do is we're gonna wanna identify the exponents. Ah, and in this case, we have an exponent of a so are longer like functions here will be equal to a ah, since when we take a log rhythm, we find the exponents. And finally we see that the solution to our exponential function here is B and that be will then belong in the parentheses of our of our log rhythmic function. So in our final log rhythmic function, so we have love based 10 of B is equal to a but the log base 10 is just a common log rhythm, so we can just rewrite this as a log of B is equal to a

So remember that if we wanted to convert an exponential equation into a log rhythmic equation well, if we have be raised to the X powers equal to K, we can convert this to our log base B okay, is equal to X. So let's do this for A and B. So for this problem or for a, we have a base of three. So you have logged based three of 10 is equal to two X and for B, we have a base of 10. So we have logged based 10 of of 0.1 is equal to negative four x. So these are our solutions. These are our solutions.

So remember that if we wanted to convert an exponential equation into large rhythmic form Well, if we have be raised to the X power is equal to K, we can rewrite this as log base B okay is equal to X and so well, you can solve a and B here. So for a are logged, we have a base of eight. We have logged based eight of 1/8 gives us a negative one. And for B, we have we have log base to of won over eight is equal to negative three. And so these these are our solutions for and be.

So the Solace First equation. What we need to do is combining these two logs on the left side. So we know that two times log of access you could tow log of x squared. So then, if we use our caution rule, he can't. Is that long of X squared to by the by seven is you go to log of 112. So then or what we can do is equate both off what's inside of the locks together. So we are excretory seventies people to want to 12. So X squared is equal to 784 where X is equal to positive 20 feet or access you go to next 20 feet. However X cannot be. You got to give 28 because X for the domain must be greater than zero. So our only solution is Xs equal to 28


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