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

1. anonymous

@Directrix

2. 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..?

3. anonymous

i dont undetstand taking the log of both sides

4. 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...?

5. anonymous

yes i understand that part

6. 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...?

7. anonymous

im sorry but i dont understand what you mean take the natural log

8. 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

9. 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.

10. anonymous

x=12?

11. campbell_st

that's it... you can check by substituting into the original equation

12. anonymous

thank you so much