Question

simplify the expression (logs)

Answer 1

\[\frac{ 12e^4 }{ 3e^7 }\]

Answer 2

lol, oops

Answer 3

\[\frac{ 4 }{ e ^{3} }\]

Answer 4

So you have two things in your problem: (1) coefficients, and (2) exponents. The coefficients form a fraction (12/3), which simplify to just 4. The exponents also form a fraction, or ratio, of (e^3/e^7). Whenever you have the same base number to a power on the top and bottom of a fraction, you can just subtract the bottom exponent from the top exponent. In this case 7-3=4, so e^3/e^7=1/e^4

Answer 5

Let me correct myself, I meant, in this case we have 3-7=-4, so e^3/e^7=e^-4. However, e^-4 is the same as 1/e^4. Any number to a negative exponent is simply the reciprocal of that number. By reciprocal I mean you put it in the bottom of the fraction, under one, as in, 1/e^4 in this case.

Answer 6

but I'm not sure how to decide whether they go to the top or the bottom

Answer 7

You can tell if the number goes on the top or the bottom depending on the sign of the exponent. In your problem if you subtract the bottom exponent from the top exponent (3-7), you get -4. Since it's negative, your exponent will go in the bottom (1/e^4).

Answer 8

3-7???

Answer 9

see its kinda simple
\[a^x \times a^y = a^{x + y}\]

\[\frac{ a^x }{ a^y } = a^{x - y}\]

see the base 'a' is same in both terms ..only the exponents differ

Answer 10

Sorry, I meant 4-7.

Answer 11

and also
\[a^{-x} = \frac{ 1 }{ a^x }\]

Answer 12

xD I was so confused... okay I get it