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anonymous
 one year ago
Find the exact solution to the equation.
320(1/4)^x/4=5
anonymous
 one year ago
Find the exact solution to the equation. 320(1/4)^x/4=5

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campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1you'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
 one year ago
Best ResponseYou've already chosen the best response.0i dont undetstand taking the log of both sides

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1ok... so if you divide both sides by 320 you get \[(\frac{1}{4})^{\frac{x}{4}} = \frac{5}{320}\] does that make sense...?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes i understand that part

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1ok... 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
 one year ago
Best ResponseYou've already chosen the best response.0im sorry but i dont understand what you mean take the natural log

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1well 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
 one year ago
Best ResponseYou've already chosen the best response.1then 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.

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1that's it... you can check by substituting into the original equation
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