Problem

Use the quotient rule for logarithms to find all …

Problem 38 Hard Difficulty

Use the product rule for logarithms to find all $x$ values such that $\log _{12}(2 x+6)+\log _{12}(x+2)=2$
Show the steps for solving.

Answer

$f(x)=0.25(3)^{x}$

Related Courses

Algebra

College Algebra

Chapter 6

Exponential and Logarithmic Functions

Section 5

Logarithmic Properties

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Video Transcript

So in this question, was asked to use the product rule of law. Algorithms were basically we have long based 12 of two X plus six first plus lovelies 12 and next we have exposed to and this is all equal to. So basically, the first thing we're gonna do is rewrite too, as long ways. 12 1 44 because 12 squared is 144. And now we know that we're adding these two together. We're just gonna drop of along based calls. Now, basically, we're actually not yet. We're gonna make this into a farm based 12 to express sex Times X plus two and now equals Bob Bates. Followed 1 44 Yeah. So now we can drop the logs and you make this to express six times X plus two equals 1 44 And I will explain. Woke span this part two x squared plus six acts Plus for extra plus 10. X Class 12 equals 1 44 It's not disappears. You put it to ax squared, watched Hannah. And then we've 12 minus 1 44 So for that, we got minus 1 32 next week. In fact, out too So we have two times X squared plus five acts and then minus 66. Now, basically, we gotta find what multiples of 66 will get us this five that we need. So 66 can be six times 11 and that's what we're gonna be using. But specifically, we need Native six times a lot because oxygen, you have 66 and it sums to five. So we have to times X plus six times X minus 11 equals zero. And now this question. What if asked us to find It's just find the X value. So these are gonna be negative wine and six and just a time These will be positive. 11 natives X man positive 11 then native sex. Now, just to check thes 11 would work because both these would be positive for negative six. We would have long based 12 native force and negative sixties. Actually, Nam bergs are actually our soul. Answer right here is gonna be 11. The reason that you're six dozen workers with his long based 12 with native six plus two is like base 12 negative floor. So we can't have that some domain flock

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