Datrys 6200=990(1115)^x+2900

$$6200 = 990 ( 1115 ) ^ { x } + 2900$$

Datrys ar gyfer x

$$x=\log_{1115}\left(\frac{10}{3}\right)\approx 0.171588967$$

Camau gan Ddefnyddio Diffiniad Logarithm

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$990\times 1115^{x}+2900=6200$$

Tynnu 2900 o ddwy ochr yr hafaliad.

$$990\times 1115^{x}=3300$$

Rhannu’r ddwy ochr â 990.

$$1115^{x}=\frac{10}{3}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(1115^{x})=\log(\frac{10}{3})$$

Logarithm rhif wedi’i godi i bŵer yw’r pŵer wedi’i lluosi â logarithm y rhif.

$$x\log(1115)=\log(\frac{10}{3})$$

Rhannu’r ddwy ochr â \log(1115).

$$x=\frac{\log(\frac{10}{3})}{\log(1115)}$$

Gyda’r fformiwla newid-sail \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$x=\log_{1115}\left(\frac{10}{3}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(1115)}+\log_{1115}\left(\frac{10}{3}\right)$$

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