I don't get this at all! I'm really horrible at these problems they are so confusing. I want to know how to do them though, so if you could go step by step that would be great!
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a^[ 3log[base a](4) ]
The key is to recognize that a^ and log[base a] are functional inverses of each other.
Two functions F(x) and G(x) are inverses of each other if F(G(x)) = G(F(x)) = x
So if F(x) = a^x and G(x) = log[base a](x),
F(G(x)) = a^[log[base a](x)] = x
So all we have to do is work on getting this to that form.
a^[3 log[base a](4) ]
Move the 3 inside of the log, to get
a^[ log[base a](4^3) ]
a^[ log[base a](64) ]
And now, the a^ and log[base a] should cancel out, leaving just
64
The key is to recognize that a^ and log[base a] are functional inverses of each other.
Two functions F(x) and G(x) are inverses of each other if F(G(x)) = G(F(x)) = x
So if F(x) = a^x and G(x) = log[base a](x),
F(G(x)) = a^[log[base a](x)] = x
So all we have to do is work on getting this to that form.
a^[3 log[base a](4) ]
Move the 3 inside of the log, to get
a^[ log[base a](4^3) ]
a^[ log[base a](64) ]
And now, the a^ and log[base a] should cancel out, leaving just
64