log(subscript 2)(0.5)

Question

I know how to convert it into:
0.5 = 2^(y)
but then how do I find y?

Answer 1

1/2 is 2 to the -1 power.

Therefore y = -1

Answer 2

How do you just know this though?

Answer 3

Because for any number a,

a^-1 = 1/a

and because 0.5 = 1/2.

These are things you know already

Answer 4

okay.

how would you solve:
2log(subscript6)(4) - (1/3)log(sub6)(8) = log(sub6)(x)

Answer 5

2log(sub6)(4) - (1/3)log(sub6)(8)
= log(sub6)(x)

log(sub6)[4^2 / 8^1/3] = log(sub6)x

log(sub6)[16/2] = log(sub6)8
= log(sub6) x

Therefore x = 8

Answer 6

so the coefficient of a log function are the same as writing it as an exponent of x in the equation: log(subb)x = y ?
therefore, Clog(subb)x = y is the same as log(subb)x^(C) = y ?

Answer 7

What you wrote is true.

Remember that log x^a = a log x, no matter what the log base is, as long as it is the same base on both sides.

However, what I am also saying is that if
Log(suba) x = Log(suba)y, then x = y

no matter what the base a is.

Answer 8

end of lesson