What is the inverse of log_{5/4}(5x-4x^2) ?

The inverse of log_{5/4}(5x-4x^2) is -(-5+sqrt(25-16(5/4)^x))/8 ,-(-5-sqrt(25-16(5/4)^x))/8

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inverse of log_{5/4}(5x-4x^2)

inverse

lo g_{\frac{5}{4}} (5 x - 4 x^{2})

- \frac{- 5 + 25 - 16 ( \frac{5}{4} ) ^{x}}{8}, - \frac{- 5 - 25 - 16 ( \frac{5}{4} ) ^{x}}{8}

Solution steps

y = lo g_{\frac{5}{4}} (5 x - 4 x^{2})

Replace

x

with

y

x = lo g_{\frac{5}{4}} (5 y - 4 y^{2})

Solve for

y, x = lo g_{\frac{5}{4}} (5 y - 4 y^{2})

- \frac{- 5 + 25 - 16 ( \frac{5}{4} ) ^{x}}{8}, - \frac{- 5 - 25 - 16 ( \frac{5}{4} ) ^{x}}{8}

f (x) = \frac{- 10 x + 1}{9 x + 6}

y = 5 (0.5)^{- x}

f (x) = \frac{( 5 x )}{x + 3}

f (x) = 1 x + 5

2 x^{2} - 4 x - 6

What is the inverse of log_{5/4}(5x-4x^2) ?
The inverse of log_{5/4}(5x-4x^2) is -(-5+sqrt(25-16(5/4)^x))/8 ,-(-5-sqrt(25-16(5/4)^x))/8