anonymous
  • anonymous
precal question
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
|dw:1450052622591:dw|
mathmale
  • mathmale
|dw:1450052701079:dw|
mathmale
  • mathmale
or is that base "y" ?

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More answers

anonymous
  • anonymous
base 4
mathmale
  • mathmale
all right. There's an important principle: the inverse function of the log function is the exponential function. have you heard or used "inverse functions" before?
anonymous
  • anonymous
ya i heard of it
mathmale
  • mathmale
Asking a related question: Can you evaluate this?
anonymous
  • anonymous
idk
anonymous
  • anonymous
still new to this lesson
mathmale
  • mathmale
\[5^{\log_{5} }27=?\]
anonymous
  • anonymous
27
mathmale
  • mathmale
Note that the base of the expo function and the base of the log function are the same. Why 27?
anonymous
  • anonymous
those 27's cancel out
anonymous
  • anonymous
i mean the 5's
mathmale
  • mathmale
Not exactly; it's the log and the expo functions that cancel out. The 5's do not cancel.
mathmale
  • mathmale
Important principle.
mathmale
  • mathmale
Going back to your posted problem, what is the base of your log system?
mathmale
  • mathmale
|dw:1450053007708:dw|
anonymous
  • anonymous
so ur left with (3x-5)=3 ?
mathmale
  • mathmale
Yes. I'd like to see all of your steps, but yes, you're right. Remove the parentheses and then solve what's left for x.
anonymous
  • anonymous
x=8 divided by 3
mathmale
  • mathmale
yes, 8/3 that's it.
anonymous
  • anonymous
ty ty ty
mathmale
  • mathmale
but it's well worth checking. How?
anonymous
  • anonymous
plug it back to the equation
anonymous
  • anonymous
(3x-5)=3
mathmale
  • mathmale
yes. if x = 8/3, what is (3x-5)?
anonymous
  • anonymous
3
mathmale
  • mathmale
right. now, is this true or false? (I'm typing something in for you)
mathmale
  • mathmale
\[\log_{4} 3=3\]
anonymous
  • anonymous
yes because of the inverse property?
anonymous
  • anonymous
principle
mathmale
  • mathmale
No, it's not correct. Good thing we checked. write this out on paper: 4 4 and then take the given expression, log to the base 4 of (3x-5) = 3 and raise those base 4's to those powers.
mathmale
  • mathmale
\[4^{\log_{4} }(3x-5)=4^3\]
mathmale
  • mathmale
Simplify this.
anonymous
  • anonymous
|dw:1450053567665:dw|
anonymous
  • anonymous
x=23
mathmale
  • mathmale
good. and so, x = ?
mathmale
  • mathmale
yes, and log to the base 4 of (3*23 - 5) = ?
anonymous
  • anonymous
64
anonymous
  • anonymous
wait.....
mathmale
  • mathmale
Yeah, but what's the log to the base 4 of 64?
anonymous
  • anonymous
|dw:1450053756960:dw|
mathmale
  • mathmale
Hint: 4^3 = 64. What is the value of |dw:1450053824754:dw|
anonymous
  • anonymous
ya its 3
mathmale
  • mathmale
what is the value of\[\log_{4}4^3 \]
mathmale
  • mathmale
So, is that good or bad in this situation?
anonymous
  • anonymous
wait is this a new problem
mathmale
  • mathmale
Note: y=log to the base 4 of x and y=4^x are inverse functions. No, same problem.
anonymous
  • anonymous
answer is 3
mathmale
  • mathmale
right. That matches your original problem statement perfectly, so x=64 is correct.
anonymous
  • anonymous
ayyyyyyyyyyyyy
mathmale
  • mathmale
Moral: Always check your work! ayyyyyyyyyyyyyyyyyyy
mathmale
  • mathmale
Morale, excuse me.
anonymous
  • anonymous
k thx
mathmale
  • mathmale
Great working with you. 'til later, then, bye!
anonymous
  • anonymous
peace out
mathmale
  • mathmale
ditto

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