Réitigh 3(1.3^x)=5

$$3 ( 1.3 ^ { x } ) = 5$$

Réitigh do x.

$$x=\log_{1.3}\left(\frac{5}{3}\right)\approx 1.947009151$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$3\times 1.3^{x}=5$$

Roinn an dá thaobh faoi 3.

$$1.3^{x}=\frac{5}{3}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(1.3^{x})=\log(\frac{5}{3})$$

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

$$x\log(1.3)=\log(\frac{5}{3})$$

Roinn an dá thaobh faoi \log(1.3).

$$x=\frac{\log(\frac{5}{3})}{\log(1.3)}$$

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

$$x=\log_{1.3}\left(\frac{5}{3}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.3)}+\log_{1.3}\left(\frac{5}{3}\right)$$

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