Datrys 592*3^2x=74

$$592 \cdot 3 ^ { 2 x } = 74$$

Datrys ar gyfer x

$$x=-\frac{3\log_{3}\left(2\right)}{2}\approx -0.94639463$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$592\times 3^{2x}=74$$

Rhannu’r ddwy ochr â 592.

$$3^{2x}=\frac{1}{8}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{2x})=\log(\frac{1}{8})$$

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

$$2x\log(3)=\log(\frac{1}{8})$$

Rhannu’r ddwy ochr â \log(3).

$$2x=\frac{\log(\frac{1}{8})}{\log(3)}$$

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

$$2x=\log_{3}\left(\frac{1}{8}\right)$$

Rhannu’r ddwy ochr â 2.

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

Datrys ar gyfer x (complex solution)

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

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