solvefor x,4^x+6^x=9^x

Solución

resolver para

x, 4^{x} + 6^{x} = 9^{x}

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{3}{2} )}

Notación decimal

x = 1.18681 \dots

Pasos de solución

4^{x} + 6^{x} = 9^{x}

Dividir ambos lados entre

4^{x}

\frac{4 ^{x}}{4 ^{x}} + \frac{6 ^{x}}{4 ^{x}} = \frac{9 ^{x}}{4 ^{x}}

Simplificar

1 + (\frac{3}{2})^{x} = (\frac{9}{4})^{x}

Aplicar las leyes de los exponentes

1 + (\frac{3}{2})^{x} = ((\frac{3}{2})^{x})^{2}

Re escribir la ecuación con

(\frac{3}{2})^{x} = u

1 + u = (u)^{2}

Resolver

1 + u = u^{2} : u = \frac{1 + 5}{2}, u = \frac{1 - 5}{2}

u = \frac{1 + 5}{2}, u = \frac{1 - 5}{2}

Sustituir hacia atrás la

u = (\frac{3}{2})^{x},

resolver para

x

Resolver

(\frac{3}{2})^{x} = \frac{1 + 5}{2} : x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{3}{2} )}

Resolver

(\frac{3}{2})^{x} = \frac{1 - 5}{2} :

Sin solución para

x \in R

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{3}{2} )}

2 7^{x + 2} = (\frac{1}{9})^{2 x + 4}

5^{x + 3} = \frac{1}{5}

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

x, 2^{x} - 2^{y} = 2016

4^{x + 2} = 7^{x - 1}