Réitigh 32^x+1=24

$$32 ^ { x + 1 } = 24$$

Réitigh do x.

$$x=\frac{\log_{2}\left(3\right)-2}{5}\approx -0.0830075$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$32^{x+1}=24$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(32^{x+1})=\log(24)$$

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

$$\left(x+1\right)\log(32)=\log(24)$$

Roinn an dá thaobh faoi \log(32).

$$x+1=\frac{\log(24)}{\log(32)}$$

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

$$x+1=\log_{32}\left(24\right)$$

Bain 1 ón dá thaobh den chothromóid.

$$x=\frac{\log_{2}\left(24\right)}{5}-1$$

Réitigh do x. (complex solution)

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

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