To solve the equation 27^x = 1/√3, both sides can be expressed as powers of 3. This leads to the equation 3^(3x) = 3^(-1/2). By equating the exponents, we find that 3x = -1/2. Solving for x gives the result x = -1/6. The solution demonstrates the method of using like bases to simplify exponential equations.
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Fright535
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I'm taking an online class and I was doing some very simple exponential equations when this was thrown at me, and I have no clue how to solve it.
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Hi,
I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance!
Question 1:
Around 4:22, the video says the following.
So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...