What is the answer to (8/9)^3*(8/9)^{-6}=(8/9)^{2x-1} ?

The answer to (8/9)^3*(8/9)^{-6}=(8/9)^{2x-1} is x=(ln(81/64))/(2ln(8/9))

Solve for x: (8/9)^3*(8/9)^{-6}=(8/9)^{2x-1}

The solution is x=(ln(81/64))/(2ln(8/9))

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(\frac{8}{9})^{3} \cdot (\frac{8}{9})^{- 6} = (\frac{8}{9})^{2 x - 1}

x = \frac{ln ( \frac{81}{64} )}{2 ln ( \frac{8}{9} )}

Decimal Notation

x = - 1

Solution steps

(\frac{8}{9})^{3} (\frac{8}{9})^{- 6} = (\frac{8}{9})^{2 x - 1}

Apply exponent rules

ln ((\frac{8}{9})^{3} (\frac{8}{9})^{- 6}) = (2 x - 1) ln (\frac{8}{9})

Solve

ln ((\frac{8}{9})^{3} (\frac{8}{9})^{- 6}) = (2 x - 1) ln (\frac{8}{9}) : x = \frac{ln ( \frac{81}{64} )}{2 ln ( \frac{8}{9} )}

x = \frac{ln ( \frac{81}{64} )}{2 ln ( \frac{8}{9} )}

3^{2 x - 2} = 81

- (\frac{5}{4}) = (\frac{- 4}{5})^{x}

2^{2} x + 3 + 7 = 15. 2^{x}

2 x - 4 = 3^{- x} + 1

2^{x} - 1 = 2^{6}

What is the answer to (8/9)^3*(8/9)^{-6}=(8/9)^{2x-1} ?
The answer to (8/9)^3*(8/9)^{-6}=(8/9)^{2x-1} is x=(ln(81/64))/(2ln(8/9))
Solve for x: (8/9)^3*(8/9)^{-6}=(8/9)^{2x-1}
The solution is x=(ln(81/64))/(2ln(8/9))