Question

1. \log_{\square} 36 = 2

\square = \square

1. find the inverse of $f(x) = 0.3^x$.

$f^{-1}(x) = \square$

1. find the inverse of $y = \log_{2} x$.

$y = \square$

Explanation:

Step1: Rewrite log as exponential

$\log_{x}36=2 \implies x^2=36$

Step2: Solve for positive base

$x=\sqrt{36}=6$
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Step1: Swap x and y for inverse

Let $y=0.3^x$, swap to $x=0.3^y$

Step2: Convert to logarithmic form

$y=\log_{0.3}x$ or $y=\frac{\ln x}{\ln 0.3}$
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Step1: Swap x and y for inverse

Let $y=\log_{2}x$, swap to $x=\log_{2}y$

Step2: Convert to exponential form

$y=2^x$

Answer:

1. $6=6$
2. $\log_{0.3}x$ (or $\frac{\ln x}{\ln 0.3}$)
3. $2^x$