Datrys e^3m+6=33

$$e ^ { 3 m + 6 } = 33$$

Datrys ar gyfer m

$$m=\frac{\ln(33)-6}{3}\approx -0.83449748$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$e^{3m+6}=33$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{3m+6})=\log(33)$$

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

$$\left(3m+6\right)\log(e)=\log(33)$$

Rhannu’r ddwy ochr â \log(e).

$$3m+6=\frac{\log(33)}{\log(e)}$$

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

$$3m+6=\log_{e}\left(33\right)$$

Tynnu 6 o ddwy ochr yr hafaliad.

$$3m=\ln(33)-6$$

Rhannu’r ddwy ochr â 3.

$$m=\frac{\ln(33)-6}{3}$$

Datrys ar gyfer m (complex solution)

$$m=\frac{i\times 2\pi n_{1}}{3}+\frac{\ln(33)-6}{3}$$

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