Question

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

Answer 1

@Directrix

Answer 2

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..?

Answer 3

i dont undetstand taking the log of both sides

Answer 4

ok... so if you divide both sides by 320 you get

\[(\frac{1}{4})^{\frac{x}{4}} = \frac{5}{320}\]

does that make sense...?

Answer 5

yes i understand that part

Answer 6

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...?

Answer 7

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

Answer 8

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

Answer 9

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.

Answer 10

x=12?

Answer 11

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

Answer 12

thank you so much