Solve: log₂ (x+9) — log₂ x = 1.

Question

Accepted Answer

hey everyone here we are asked to solve for y. And we have the equation log base five of Y plus 96 minus log base five of y is equal to two. And now we can start by first making this second term, the second log positive by adding log base five of y to both sides. Now rewriting we have log base five of Y plus 96 is equal to two plus log base five of Y. And our next step here is to change this to into a log so that we can actually make more simplifications. So doing this, we need to recall that one is equal to log base A. Of A. And now we have a two that we're trying to replace. So we need to multiply both sides by two. So we have two is equal to two times log base A. Of A. And now we need to note that in our equation here we have log with a base of five so our A. Is going to be five so we'll have two is equal to two times log base five of five. And now we can input this information into our equation. Rewriting, we have log base five of y plus 96 is equal to instead of two. We now have two times log base five of five plus log base five of y. And next we can start simplifying a little further we have again log base five of Y plus 96 is equal to. And now with this next term here we need to recall that when we have a coefficient of the log we can take the term that's in the parentheses. And put it to the power of the coefficient here. So doing this we have log base five of five to the power of two plus log base five of y. And now just simplifying a little further again we have log base five of y plus 96 is equal to log base five of 25 plus log base five of y. Next we can make a further simplification to the right hand side by recalling that when we add logs of the same base, we can multiply their terms together. So doing this again, we have log base five of y plus 96 is equal to log base five and now multiplying their terms together. We have 25 times why? And now since both of these logs have the same base of five, we can just write the terms inside the parentheses as its own equation. So we can just have Y plus 96 B equal to 25 Y. And with this we can easily solve for y. So we first subtract Why from both sides we have 96 is equal to 24. Y dividing both sides by 24. To get Y alone, we see that Y is equal to four. And with that we are left with answer choice. A thanks for watching. I hope you found this video helpful and I'll see you again next time.

Solve: log₂ (x+9) — log₂ x = 1.

Key Concepts

Logarithmic Properties

Exponential Form

Domain of Logarithmic Functions

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