Please find 'x' in this case.? Exponents chapter!?

Question

9^x+^2 = 240 + 9^x

Answer 1

9^x + x^2 = 240 + 9^x
Subtract 9^x from both sides of the equation.
x^2 = 240
Use the square root theorem: If a^2 = b, then a = +o- sqrt(b).
x = +or- sqrt(240)
x = sqrt(240) or x = -sqrt(240)
x = sqrt(16)sqrt(15) or x = -sqrt(16)sqrt(15)
x = 4sqrt(15) or x = -4sqrt(15)

or

9^(x + 2) = 240 + 9^x
(9^x)(9^2) =240 + 9^x
81(9^x) = 240 + 1(9^x)
80(9^x) = 240
9^x = 3
(3^2)^x = 3
3^(2x) = 3^1
If bases are equal, then exponents are equal.
2x = 1
x = 1 / 2

Answer 2

Your equation is not clear. is it 9^(x+2) = 240 + 9^x? If so, then realize 9^(x+2) is the same as (9^2)*(9^x), so the equation becomes

9^2 * 9^x = 240 + 9^x

Move the right-hand 9^x to the left

9^2 * 9^x - 9^x = 240

factor out the 9^x

9^x * (9^2 - 1) = 240

9^x = 240/80 = 3

Now take log of both sides:

x*log(9) = log(3)

x = log(3)/log(9) = 0.477/0.954 = 0.5

You can also do this by realizing 3 = 9^(0/5)

then 9^x = 9^0.5, so x = 0.5 (matching exponents)

Answer 3

Your question is written incorrectly.

If it is 9^x + x^2 = 240 + 9^x then

x^2 = 240

x = sqrt(240) = 15.49193

If it is 9^x+2 = 240 + 9^x then

9^x+2 - 9^x = 240

9^2 - 1 = 240 / 9^x

80 = 240 / 9^x

9^x = 240/80

9^x = 3

x = 1/2

If it is neither of these, please correct it.

Answer 4

my dear your que. was a littel ambiguous to me.....if it is 9^x*9^2=240+9^x the first step is that: 9^x*9^2-9^x=240
factor: 9^x(9^2-1)=240
then we have : 9^x(81 -1)=240
9^x(80)=240
then: 9^x=3
you can change 9 into 3^2
so we have: 3^2x=3
the bases are the same ,so the powers should be the same:
2x=1
so.............. x=1/2

Answer 5

i am sorry i am only young (in secondary school) and i have no idea i have tried but it is too hard and what does ^ mean because i thought it means to the power of but i dont know

Answer 6

no answer