Datrys 1.5*(1.07)^x=4

$$1.5 \times ( 1.07 ) ^ { x } = 4$$

Datrys ar gyfer x

$$x=\log_{1.07}\left(\frac{8}{3}\right)\approx 14.496731388$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$1.5\times 1.07^{x}=4$$

Rhannu dwy ochr hafaliad â 1.5, sydd yr un peth â lluosi’r ddwy ochr â chilydd y ffracsiwn.

$$1.07^{x}=\frac{8}{3}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(1.07^{x})=\log(\frac{8}{3})$$

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

$$x\log(1.07)=\log(\frac{8}{3})$$

Rhannu’r ddwy ochr â \log(1.07).

$$x=\frac{\log(\frac{8}{3})}{\log(1.07)}$$

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

$$x=\log_{1.07}\left(\frac{8}{3}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.07)}+\log_{1.07}\left(\frac{8}{3}\right)$$

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