# Search results

1. ### Exponential/logarithmic equation

After a while, i finaly got to this equation, and solved it. It was quite easy. x*3^{log_{x}5}=15 /multiply this with log of base 3 log_{3}x + log_{x}5 = log_{3}5 + 1 when you convert log_{x}5 to base 3, and and multiply the whole equation with log_{3}x and sort it out, factorize, you...
2. ### Find a value of the angle from the given equation

I thought i made it clear - yes, it is tangentg of x. As i said, i already knew that alpha=arctg of the right side. But i need how to exactly GET the value of alpha. I hope you understand where i'm going at? How much is alpha - in degrees - rather than it is arctg of the expression on...
3. ### Find a value of the angle from the given equation

it is tg(alpha), and alpha is in the first quadrant! also, i need the exact size, in degrees.
4. ### Cartesian product help?I'm interested how to solve the following problem:

actually that was the key to solving this, but i found a version of this task where it said (a+b+c)X(a+b-c), and i was in doubt what X means, and i thought it was a vector product. however, it turned out to be just simple ol' multiplying.
5. ### Find a value of the angle from the given equation

Homework Statement If we are given an equation that equals tg\alpha, and we need to find out how much is \alpha, how would we do it, having in mind the equation bellow? Homework Equations tg\alpha=\frac{(1+tg1)(1+tg2)-2}{(1-tg1)(1-tg2)-2} The Attempt at a Solution Since i know the answer (i...
6. ### Cartesian product help?I'm interested how to solve the following problem:

I know the law of cosines, but i can't find a way to use it here, because i don't know the numerical values of the pages, neither do i know the angles. I just know i have the condition given that (a+b+c)x(a+b-c)=3ab. I'm guessing that x marks the Cartesian product of a+b+c and a+b-c and...
7. ### Cartesian product help?I'm interested how to solve the following problem:

i messed up the post. check the edited version.
8. ### Cartesian product help?I'm interested how to solve the following problem:

I'm interested how to solve the following problem: if we have a triangle, where a,b,c are sides of that triangle and we know that (a+b+c)x(a+b-c)=3ab, we need to find the angle opposite to side c. How to do this?
9. ### Exponential/logarithmic equation

:biggrin: I appreciate you all helping. I see some of you suggested hit/miss option, that i want to avoid. I'm interested if anyone could provide a procedure that's not based on guessing (but if we're at it - 5 is one of the solutions :D). I'll keep on trying and if i come up with...
10. ### Exponential/logarithmic equation

3^\frac{log_{3}5}{log_{3}x} would be \frac{log_{3}5}{x} because 3^{\log_3(x)} is x?
11. ### Exponential/logarithmic equation

I could write 3^{log_{x}5} as 3^\frac{1}{log_{5}x} or 3^\frac{log_{c}5}{log_{c}x}, where c is some other constant, but i don't know what to do with the x that multiplies 3, that's what's causing me trouble.
12. ### Exponential/logarithmic equation

I know those formulas, but i didn't find a way to properly use them in this case. Also, i'm sorry if i posted this inf the wrong forum. Mods can move the topic.
13. ### Exponential/logarithmic equation

Homework Statement How many numbers, where x is is a whole number, satisfy the equation. Homework Equations x*3^{log_{x}5}=15 The Attempt at a Solution Most of my attempts have been blocked due to the fact that i don't know what to do with the x that is not in the base of algorithm. I tried...
14. ### Finding a i b

It's possible if c and d are both equal zero! Then i just solve the system of 2 equations with 2 unknowns. THANKS gb7nash! (hate it when i miss obvious catches)...
15. ### Finding a i b

The key word would be somehow. If multiplication worked, i wouldn't be asking how :). Anyway, i get a bunch of junk, and i can't seem to figure out what to do with it. How to create or find 3a-7b, that is...
16. ### Finding a i b

If a and b are real numbers, and we know that (2a-b-3)^{2} + (3a+b-7)^{2}=0, how much is 3a-7b Any ideas on this? I'm guessing the solution can go two ways: either i find a and b separately, or i calculate the expression above somehow and i'll be left with 3a-7b
17. ### Question about complex numbers

well, that was my idea originally. using the facts that i^{1}=i, i^{2}=-1, i^{3}=-i, i^{4}=1 i tried to find a way to brake the expression given in the first post into something which could destroy the [te]i[/tex], just like i would do with, ie (1+i)^{2010}=(2i)^{1005}=2^{1005}i, but i'm...
18. ### The number of complex numbers that satisfy the equation

I made an error while copying the original equation, and partly copying my idea, fixed it in the original post now. I think my first step is okay now, having in mind changes i made? It's important that this is the right way. I'll just finish it, i guess i made a mistake in the calculus...
19. ### The number of complex numbers that satisfy the equation

Homework Statement So, i have this equation, and it is asked of me to find the number of complex numbers that satisfy the equation. (z=x+iy) Homework Equations z-\overline{z}+|z-i|=4-2i The Attempt at a Solution I tried replacing the numbers and i got something like this...
20. ### Question about complex numbers

Hello guys! I have a question related to complex numbers. How would i calculate, for example (\frac{\sqrt{3}+i}{2})^{2010} without using the De Moivre's theorem?