Datrys 7^x=47

$$7 ^ { x } = 47$$

Datrys ar gyfer x

$$x=\log_{7}\left(47\right)\approx 1.97858447$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$7^{x}=47$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(7^{x})=\log(47)$$

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

$$x\log(7)=\log(47)$$

Rhannu’r ddwy ochr â \log(7).

$$x=\frac{\log(47)}{\log(7)}$$

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

$$x=\log_{7}\left(47\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(7)}+\log_{7}\left(47\right)$$

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