log(subscript 2)(0.5)
I know how to convert it into:
0.5 = 2^(y)
but then how do I find y?
1/2 is 2 to the -1 power.
Therefore y = -1
How do you just know this though?
Because for any number a,
a^-1 = 1/a
and because 0.5 = 1/2.
These are things you know already
okay.
how would you solve:
2log(subscript6)(4) - (1/3)log(sub6)(8) = log(sub6)(x)
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
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 ?
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.
end of lesson
To find the value of y in the equation 0.5 = 2^y, you need to take the logarithm of both sides of the equation. Since the base of the exponent is 2, you would take the logarithm with base 2 of both sides.
Using the logarithmic property log(subscript b)(x^y) = y * log(subscript b)(x), we can rewrite the equation as:
log(subscript 2)(0.5) = y * log(subscript 2)(2)
Since log(subscript b)(b) = 1 for any base b, we know that log(subscript 2)(2) = 1. Therefore, the equation simplifies to:
log(subscript 2)(0.5) = y
Now, to evaluate the logarithm on the left-hand side, you can use a scientific calculator or software that has a logarithm function. Simply input 0.5 as the argument and choose the logarithm function base 2 (log(subscript 2)). The result will be the value of y.