Réitigh 100*2^4x=15

$$100 \cdot 2 ^ { 4 x } = 15$$

Réitigh do x.

$$x=\frac{\log_{2}\left(\frac{3}{5}\right)}{4}-\frac{1}{2}\approx -0.684241399$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$100\times 2^{4x}=15$$

Roinn an dá thaobh faoi 100.

$$2^{4x}=\frac{3}{20}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(2^{4x})=\log(\frac{3}{20})$$

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

$$4x\log(2)=\log(\frac{3}{20})$$

Roinn an dá thaobh faoi \log(2).

$$4x=\frac{\log(\frac{3}{20})}{\log(2)}$$

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

$$4x=\log_{2}\left(\frac{3}{20}\right)$$

Roinn an dá thaobh faoi 4.

$$x=\frac{\ln(\frac{3}{20})}{4\ln(2)}$$

Réitigh do x. (complex solution)

$$x=\frac{\pi n_{1}i}{2\ln(2)}+\frac{\log_{2}\left(\frac{3}{20}\right)}{4}$$

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