ah right cheers.
This is bit of a "simple" question however just looking back at logs i seem to have forgotten a few things.
e.g. if log2(5) = log2(5) , why can the log 2 cancel out and x = 5.
this brings me to x = log2(5)/log2(6) , why cannot the answer be 5/6?
Let's use an analogy. Consider the function y=f(x), and let's also assume it is a one-to-one function (just like the logarithmic and exponential functions).
=f(5))
This is because with a one-to-one function, every x value maps to a unique y value. That is, the value 'f(5)' can only be obtained by subbing in 5 into f(x). This is not the case for many-to-one functions -- consider
=x^2)
for example. g(2)=4, but you'll see that both x=2 and x=-2 will give us this same y-value.
Because the logarithm is a one-to-one function, every x value must then map to a unique y value.
Let's go back to your example:
=\log_{2}(5))
The only way to get to a
value of
)
using a logarithm of base 2 is if the
value is 5.
Okay great. Let's look at
}{f(6)})
.
Hopefully, you're aware that
}{f(6)} \neq \frac{5}{6})
. Well I mean it
could under some cases equal that (for example, if f(x)=x), but generally this isn't going to hold true. The same applies to logarithms -- they are a function like any other, so you can't just do what you did.
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