Datrys 3(1.3^x)=5

$$3 ( 1.3 ^ { x } ) = 5$$

Datrys ar gyfer x

$$x=\log_{1.3}\left(\frac{5}{3}\right)\approx 1.947009151$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3\times 1.3^{x}=5$$

Rhannu’r ddwy ochr â 3.

$$1.3^{x}=\frac{5}{3}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(1.3^{x})=\log(\frac{5}{3})$$

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

$$x\log(1.3)=\log(\frac{5}{3})$$

Rhannu’r ddwy ochr â \log(1.3).

$$x=\frac{\log(\frac{5}{3})}{\log(1.3)}$$

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

$$x=\log_{1.3}\left(\frac{5}{3}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.3)}+\log_{1.3}\left(\frac{5}{3}\right)$$

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