How do you find the inverse of $f (x) = {log 2}^{x}$ $f(x) = log 2^x$ ?

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How do you find the inverse of $f (x) = {log 2}^{x}$ $f(x) = log 2^x$ ?

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Answer 1 · 2016-01-26T06:09:18

$f^{- 1} x = \frac{x}{log 2}$ $f^-1x=x/log2$

Explanation:

If a given equation is $f (x) = y$ $f(x)=y$ then the inverse of that function is $f^{- 1} (y) = x$ $f^-1(y)=x$

Now, given $f (x) = {log 2}^{x} \Rightarrow y = {log 2}^{x}$ $f(x)=log2^x\impliesy=log2^x$

I'm sure you know this general log formula ${log}_{n} m^{l} = l {log}_{n} m$ $log_nm^l=llog_nm$
So applying this the the equation above, $y = x log 2$ $y=xlog2$

So that means $\frac{y}{log 2} = x$ $y/log2=x$ and fora fact, we know that $f^{- 1} (y) = x$ $f^-1(y)=x$ , so $f^{- 1} y = \frac{y}{log 2}$ $f^-1y=y/log2$

Just replace $y$ $y$ with $x$ $x$ to get the general formula

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How do you find the inverse of $f (x) = {log 2}^{x}$ $f(x) = log 2^x$ ?

1 Answer

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How do you find the inverse of $f (x) = {log 2}^{x}$ $f(x) = log 2^x$ ?