Gleichung lösen: 4^{x - 2} = 5^{x/2}

Question

Lösen Sie die Gleichung 4^{x-2} = 5^{x/2}

Answer 1

4^{x - 2} = 5^{x/2}

1/16·4^{x} = 5^{x/2}

1/16·16^{x/2} = 5^{x/2}

(16/5)^{x/2} = 16

x/2 = LN(16) / LN(16/5)

x = 2·LN(16) / LN(16/5) = 4.767376162

Answer 2

4^{x - 2} = 5^{x/2}
( x - 2) * ln (4) =  x/2 * ln(5)
( x - 2 ) / x = ln(5) / ( ln(4) * 2)
1 - 2 / x = 0.5805
2 / x =0.4195
x = 4.768

mfg Georg