Question

4^x=16^x-3

Answer 1

Are we simplifying this?

Answer 2

yes

Answer 3

You got any choices to choose from.

Answer 4

no i do not it just said i should solve for x by getting the same base( do not use logs)

Answer 5

This is the answer I got 0.72135

Answer 6

how did you solve it?

Answer 7

I used logs.

Answer 8

okay thank you and i have one last question. Nowtown is growing consistently at a rate of 2.8% per year. If there were 700 people initially, how many years will it take for there to be 2000 people? round your answer to 2 decimal places

Answer 9

Is your question perhaps 4^x = 16^(x - 3)?

Answer 10

For the second question, it might be best to find the general formula of the population.
Year 0: 700 people
Year 1: 700 + 700 * 2.8% = 700(1 + 2.8%) = 719.6 people
Year 2: 719.6 + 719.6 * 2.8% = 719.6(1 + 2.8%) = 700(1 + 2.8%)(1 + 2.8%)
= 700(1 + 2.8%)^2 = 739.7488 people
From these, you can see that the population of Nowtown is given by
700(1 + 2.8%)^t where t is the number of years.
Now that you have an equation, you can set it to 2000 and solve for t.
2000 = 700(1 + 2.8%)^t
I assume you know how to solve this using logarithm.