Datrys 5^y=16

$$5 ^ { y } = 16$$

Datrys ar gyfer y

$$y=4\log_{5}\left(2\right)\approx 1.722706232$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$5^{y}=16$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{y})=\log(16)$$

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

$$y\log(5)=\log(16)$$

Rhannu’r ddwy ochr â \log(5).

$$y=\frac{\log(16)}{\log(5)}$$

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

$$y=\log_{5}\left(16\right)$$

Datrys ar gyfer y (complex solution)

$$y=\frac{2\pi n_{1}i}{\ln(5)}+4\log_{5}\left(2\right)$$

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