exponent problem

[NGard]

I would be extremely grateful if someone could help with a simple seeming issue I ran into and cannot seem to nail down.

8^n = 200
(or eight raised to the power of n equals 200)

How do i solve for n?
It seems like it should be easy but I can't see it.

Thanks,
Nick

 

[passionflower_40]

I would be extremely grateful if someone could help with a simple seeming issue I ran into and cannot seem to nail down.

8^n = 200
(or eight raised to the power of n equals 200)

How do i solve for n?
It seems like it should be easy but I can't see it.

Thanks,
Nick

8^n=200 in order to factor an integer we need to divide by the prime number
which is 2
(2^3)^n=200 next we will need to exponentiate the power. The following rule is
(a^b)^c= a^bc

2^3n=200 since there is no variables in this equation, all terms can be
transferred to the left side.
2^3n-200=0 <---this is your answer

 

[stapel]

2^3n-200=0 <---this is your answer

:shock:

Um... no, not really....

Since 200 is not a power of 2, as 8 is, then you can't compare exponents to solve. You'll have to use logarithms to find an approximate solution.

So start by taking logs of either side. (You can use whatever base you like, but base-10 or base-e would be best, since you can then plug this into your calculator later.)

Use the power-in-a-log rule to get the "n" outside of the logarithm, and then divide through by the log factor to isolate the variable.

When you're done, your solution should evaluate to approximately 2.55.

Eliz.