Réitigh 3^23*3^x*3^19=3^78

$$3 ^ { 23 } \times 3 ^ { x } \times 3 ^ { 19 } = 3 ^ { 78 }$$

Réitigh do x.

$$x=36$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Úsáid rialacha na n-easpónant agus na logartam chun an chothromóid a réiteach.

$$109418989131512359209\times 3^{x}=16423203268260658146231467800709255289$$

Roinn an dá thaobh faoi 109418989131512359209.

$$3^{x}=150094635296999121$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(3^{x})=\log(150094635296999121)$$

Is ionann logartam uimhreacha a ardaítear go cumhacht agus an chumhacht méadaithe faoi logartam na huimhreach.

$$x\log(3)=\log(150094635296999121)$$

Roinn an dá thaobh faoi \log(3).

$$x=\frac{\log(150094635296999121)}{\log(3)}$$

Leis an bhfoirmle athrú boinn \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$x=\log_{3}\left(150094635296999121\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+36$$

$$n_{1}\in \mathrm{Z}$$