Réitigh {left(1+3.2/100right)}^x=200

$${ \left(1+ \frac{ 3.2 }{ 100 } \right) }^{ x } =200$$

Réitigh do x.

$$x=\log_{1.032}\left(200\right)\approx 168.207669123$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Fairsingigh \frac{3.2}{100} tríd an t-uimhreoir agus an t-ainmneoir araon a iolrú faoi 10.

$$\left(1+\frac{32}{1000}\right)^{x}=200$$

Laghdaigh an codán \frac{32}{1000} chuig na téarmaí is ísle trí 8 a bhaint agus a chealú.

$$\left(1+\frac{4}{125}\right)^{x}=200$$

Suimigh 1 agus \frac{4}{125} chun \frac{129}{125} a fháil.

$$\left(\frac{129}{125}\right)^{x}=200$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(\left(\frac{129}{125}\right)^{x})=\log(200)$$

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

$$x\log(\frac{129}{125})=\log(200)$$

Roinn an dá thaobh faoi \log(\frac{129}{125}).

$$x=\frac{\log(200)}{\log(\frac{129}{125})}$$

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

$$x=\log_{\frac{129}{125}}\left(200\right)$$

Réitigh do x. (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.032)}+\log_{1.032}\left(200\right)$$

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