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

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

Mathematics
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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..?
i dont undetstand taking the log of both sides

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ok... so if you divide both sides by 320 you get \[(\frac{1}{4})^{\frac{x}{4}} = \frac{5}{320}\] does that make sense...?
yes i understand that part
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...?
im sorry but i dont understand what you mean take the natural log
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
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.
x=12?
that's it... you can check by substituting into the original equation
thank you so much

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