Video

3(81^x) = 6 81^x = (6/3) = 2 log 2 / log 81 = 0.157732438 81^ 0.157732438 = 1.999999997 1.999999997 x 3 = 5.999999999

Before watching: This will go most easily if we square away the radicals on the left. Recall that a^(mn) = (a^m)^n. First, square the left and the right, to get 3sqrt(9 sqrt(27)) = 81^(6x) = 3^(24x) (because 3^4=81) Squaring again we get (3^2)(9)sqrt(27) = 81 sqrt(27)= 81^(12x) And with one last squaring... (81^2)(27) = 81^(24x). Since 81 = 3^4, 27 = 3^3, and (a^m)(a^n) = a^(m+n)... (3^4)^2 * 3^3 = (3^4)^(24x) -> 3^11 = 3^(96x). Then 11 = 96x, and finally x = 11/96

Go away

C

7/16 in mind

Rather than squaring expressions I converted them to exponential form right away: On the left 3^1/2 x 9^1/4 x 27^1/8, all powers of 3; on the right 3^12x. Add exponents on the left to get 11/8 with 12x on the right. X = 11/96.

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Substitute a=b+1/2. (b+1/2)^4-(b-1/2)^4=2[4b^3(1/2)+4b(1/8)]=0 b^3+b/4=0. b=0 or b=±i/2. a=1/2 or (1±i)/2

the right answer is 262143

what a waste of time

Mate, you are among the 99% who got it wrong.

0:10 111111111111111111 but in base 2

I don't get it. Why not say 262144 - 1 ? If you are going to take the step that 512 is 2 to the ninth, why not say that 2 to the eighteenth is 262144 ?

This is super-stupid. If you know that 2^9 is 512, you could just do 512^2 - 1...factoring it into (512+1)(512-1) is the single dumbest way you could go about solving from there. But then you do a whole bunch of other time-wasting after.

oxymoron

Just do multiplication by 2 manually lol

2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,131072,262144 (2^18) So 262143.

It really is not that difficult toto just multiply 511 x 513 which equals 262,143.

Yes😂😂😂😂

I am afraid that the final sum is wrong.

X=0

ITNA LAMBA Q KIYA? 4^8/8^4 - 8^4/4^8 can also be written as 64*64*16/64*64 - 64*64/64*64*16 sare 64 cut jayenge, simple bachega 16 - 1/16 = (265-1)16 =255/16

The easiest solution is to put everything in powers of 2. You then have 2^2^8 / 2^3^4 - 2^3^4 / 2^2^8 = 2^16/2^12 - 2^12/2^16 = 2^4 - 1/2^4 = 16 - 1/16 = 255/16.

45 = 3^3.465...rien de plus simple

sqrt(10 * sqrt(10 * sqrt(10))) = 100^x (10 * (10 * 10^(1/2))^(1/2))^(1/2) = 10^2x 10 * (10 * 10^(1/2))^(1/2) = 10^4x 100 * 10 * 10^(1/2)) = 10^8x 10 000 * 100 * 10 = 10^16x 10 000 000 = 10^16x 10^7 = 10^16x 7 = 16x 7/16 = x x = 7/16 = 0,4375

He wastes time on several steps. 3^x = 45 can immediately be re-written as log_3 (45) = x. We're not required to use log base 10 to eventually get to this step.

Dividing by 2 at the beginning was unnecessary.

If 99% of entrants failed this they never learned arithmetic.

2 *sqrt(x) = x. One solution is zero. For the other, divide by sqrt(x) to get 2 = sqrt(x). That means x = 4, the other solution.

I don't believe 99% would fail to find the 0 solution. You wouldn't clickbait, would you?

I literally just looked at it and knew 3⁴ + 3² = 90. You REALLY overcomplicated it

Nearby value?

Can any suggest what is value of x? In rational

3²+3⁴=90, but answer is 9×5+9×5=45+45=90 because we have to so how much we can remember and show that why 3×3×3×3+×3×3 is 90 Which we never use in our life. I am not telling that math and science is useless be this this 💀😕 education system crush it and fuck it

3^x=45, 3^(x-2)=5, (x-2) log 3 = log 5, x=2+(log 5)/(log 3). If 99% failed this, the population had never learned about logarithms.

easy toh hai😂😂

x=4 and possibly imaginary values

If we divide by √x, we get 2=√x i.e. x=4. But the equation has one more solution (when division is invalid): x=0. (If x is negative, then √x is imaginary. More generally, if x is complex other than a positive real number, then angle of √x in polar coordinates can't be the same as the angle of x.) We can also substitute y=√x; then we get y^2 - 2*y = 0, and that yields y*(y-2)=0, immediately giving the two solutions (a quadratic equation can't have more than two solutions).

Nice calculating. But how on earth are you writing the letter "x"?

1:27 x^3 + x^2 + x - 555 = 0👀 1 1 1 -155 Syntetic division 5 5 30 155 1 6 31 0 x^2 + 6x + 31=0 D1=(b/2)2-ac=3^2-1*31 < 0

Acho que está errado essa resolução.

Isn't that not simple 7+49+343+2401+16807 = 19607

25

B 25

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Silly soundtrack. Left after 20 seconds

Oh wow thank you

Isn't that just a simple sum of gp?

Muito legal!

5^2/25^2 = (5/25)^2 = (1/5)^2 = 1^2/5^2 =1/25