Réitigh {left(1+32/100right)}^x=200

$${ \left(1+ \frac{ 32 }{ 100 } \right) }^{ x } =200$$

Réitigh do x.

$$x=\log_{\frac{33}{25}}\left(200\right)\approx 19.083975886$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Laghdaigh an codán \frac{32}{100} chuig na téarmaí is ísle trí 4 a bhaint agus a chealú.

$$\left(1+\frac{8}{25}\right)^{x}=200$$

Suimigh 1 agus \frac{8}{25} chun \frac{33}{25} a fháil.

$$\left(\frac{33}{25}\right)^{x}=200$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(\left(\frac{33}{25}\right)^{x})=\log(200)$$

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

$$x\log(\frac{33}{25})=\log(200)$$

Roinn an dá thaobh faoi \log(\frac{33}{25}).

$$x=\frac{\log(200)}{\log(\frac{33}{25})}$$

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

$$x=\log_{\frac{33}{25}}\left(200\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{33}{25})}+\log_{\frac{33}{25}}\left(200\right)$$

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