please help me before tommorow. I have 2 questions for math lovers?

Question

1. if 9^x+2___=____240___*____ 9^x
then find the value of x

2. if 4^x____-____ 4^x-1_______=_______ 24
then find the value of (2x)^x


(underscores are put to make it clear. even a small help will be appreciated.)

Answer 1

Hi,

1. 9^(x+2)=240_*_ 9^x

If we converted 240 into 9 to a power, the equation would be:

9^y = 240

Taking the log of each side gives:

log 9^y = log 240
y * log 9 = log 240
y = log 240/ log 9
y = 2.4943

Changing 240 to 9^2.4942 changes the equation from:
9^(x+2)=240_*_ 9^x to:
9^(x+2)=9^2.4943_*_ 9^x
9^(x+2)=9^(x+2.4943)

This means 2 = 2.4943, which isn't true. Therefore, there is no solution to this problem.

2. 4^x_-_ 4^x-1_=_ 24

If you enter Y1 = 4^x - 4^(x-1) - 24 into your calculator and solve for the zero, you will discover that it is when x = 5/2.

This can be verified by saying:

4^x - 4^(x-1) = 24

4^(5/2) - 4^(5/2 -1) = 24

4^(5/2) - 4^(3/2) = 24
(√4)^5 - (√4)³ = 24
2^5 - 2³ = 24
32 - 8 = 24
24 = 24

So, x = 2.5. That means that (2x)^x = (2*2.5)^2.5 = 55.9017

I hope that helps!! :-)

Answer 2

These are not hard; however it shows you have a homework assignment due and you have not studied. Giving you the answer will not teach you and you will not be able to pass the exam either.

Master the material and do you own homework.

Answer 3

cant agree more with GTB. having a grade for a perfect homework will mean nothing f you score a zero on your exam!