Logarithms Definition and 257 Threads

Hello, The following problem is bothering me quite a bit. It is... Solve. 3 x 2^x = 12 The Unit this question is in is about solving exponential equations through expressing each side as a power of the same base, by taking a base (x) logarithm of each side or taking a base 10 logarithm...

IS there a way to find x if given: 3^x - 3^(x-1) = 1000 I tried to take log [3^x - 3^(x-1)]/log[3] = log1000/log3 but then, x-x-1 = ...

Okay. "Solve the exponential equation with base a algebraically. Approximate the result to three decimal places." 3^2x=80 (fyi, the answer is ln80/2ln3 = 1.994) Don't understand how to solve, please help!

Hi, I have a couple of problems that involve solving exponential equations using logarithms. One of them I got an answer but I'm not positive whether I did it right, and one of them I have no idea... 3^(4logx)= 5 (4logx)log3=log5 logx=log5/4log3 logx=.698/1.91 logx=.365 10^.365=x...

Hi all, I wonder what is the best way to introduce logarithms when you're teaching. My "approach #1" is the one I consider the most natural: You introduce exponential functions as f(x) = bx, and ask what is the derivative. It turns out df/dx = lim(h->0) (bh-1)/h bx. Now, actually ln(b)...

I'm having trouble with these type of probles (where a negative log comes up): (All of this is solving without sigma notation) Find the number of terms in these geometric sequences and the sum of the numbers. 11, -22, 44,...,704 I know that a1 = 11, r = -2, and an = 704, so I did...

I need help on a lograrith HM: Solve for X: log(x-1)=log(x-2)-log(x+2) I got till here: log(x-1)=(log(x-2)/(x+2)) Donot know what to do after wards ***Hey if you could tell me the answer please tell me how you derived it. i want to understand the problem. And Base if course to the 10.