anonymous
  • anonymous
Find the exact solution to the equation. 320(1/4)^x/4=5
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
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
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@Directrix
campbell_st
  • campbell_st
you'll need logs start by dividing both sides of the equation by 320 then take the log of both sides then apply the log laws for powers... does that make sense..?
anonymous
  • anonymous
i dont undetstand taking the log of both sides

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

campbell_st
  • campbell_st
ok... so if you divide both sides by 320 you get \[(\frac{1}{4})^{\frac{x}{4}} = \frac{5}{320}\] does that make sense...?
anonymous
  • anonymous
yes i understand that part
campbell_st
  • campbell_st
ok... so take the natural log of both sides or you can look at it this way \[(\frac{1}{4})^\frac{x}{4} = \frac{5}{320}~~~~or~~~~(\frac{1}{4})^{\frac{x}{4}} = \frac{1}{64}\] does that make sense...?
anonymous
  • anonymous
im sorry but i dont understand what you mean take the natural log
campbell_st
  • campbell_st
well if you want to do the solution with logs you can... but what I have posted is an alternate method. using Logarithms is the most obvious method... but using the alternate method you have \[(\frac{1}{4})^\frac{x}{4} = \frac{1}{64}\] so write the right hand side of the equation as a power with a base of 1/4
campbell_st
  • campbell_st
then you get \[(\frac{1}{4})^{\frac{x}{4}} = (\frac{1}{4})^3\] now you have the same base, you can equate the powers and solve for x.
anonymous
  • anonymous
x=12?
campbell_st
  • campbell_st
that's it... you can check by substituting into the original equation
anonymous
  • anonymous
thank you so much

Looking for something else?

Not the answer you are looking for? Search for more explanations.