Solve for x. 3600=400(2^10x)

Question

Answer 1

We're going to use log rules to solve this problem. The basic log rule that you need is that log(a^b) = b*log(a).

Starting with 3600 = 400*2^10x

Divide both sides by 400 to get:

9 = 2^10x

Now, take log of both sides:

log(9) = log(2^10x)

Use the log rule to bring the exponent down:

log(9) = 10x*log(2)

Divide both sides by log(2):

10x = log(9)/log(2)

Then divide both sides by 10:

x = (1/10)*log(9)/log(2)

I hope this helps!

Answer 2

3600 = 400*2^10x (Isolate the x variable by doing the inverse function - Divide by 400)

9 = 2^10x (Take ln of both sides and use ln(y^z) = zln(y))

ln(9) = 10x*ln(2) (Divide by 10ln(2))

ln(9)/(10ln(2)) = x

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