# logarithmic functions

log(subscript 2)(0.5)

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

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1. 1/2 is 2 to the -1 power.

Therefore y = -1

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2. How do you just know this though?

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3. Because for any number a,

a^-1 = 1/a

and because 0.5 = 1/2.

These are things you know already

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4. okay.

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

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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

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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 ?

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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.

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8. end of lesson

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