What is the inverse of log_{1/3}((5-x)/x) ?

The inverse of log_{1/3}((5-x)/x) is 5/((1/3)^x+1)

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inverse of log_{1/3}((5-x)/x)

inverse

lo g_{\frac{1}{3}} (\frac{5 - x}{x})

\frac{5}{( \frac{1}{3} ) ^{x} + 1}

Solution steps

y = lo g_{\frac{1}{3}} (\frac{5 - x}{x})

Replace

x

with

y

x = lo g_{\frac{1}{3}} (\frac{5 - y}{y})

Solve for

y, x = lo g_{\frac{1}{3}} (\frac{5 - y}{y})

\frac{5}{( \frac{1}{3} ) ^{x} + 1}

3 x + 4 y = 9

(x + 5) e^{- 2 x}

f (x) = - x^{2} + 4

f (x) = \frac{( x ^{2} - 4 )}{x + 2}

f (x) = sin (2 x)

What is the inverse of log_{1/3}((5-x)/x) ?
The inverse of log_{1/3}((5-x)/x) is 5/((1/3)^x+1)