Datrys 15^x=10^5

$$15 ^ { x } = 10 ^ { 5 }$$

Datrys ar gyfer x

$$x=5\log_{15}\left(10\right)\approx 4.251370769$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$15^{x}=100000$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(15^{x})=\log(100000)$$

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

$$x\log(15)=\log(100000)$$

Rhannu’r ddwy ochr â \log(15).

$$x=\frac{\log(100000)}{\log(15)}$$

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

$$x=\log_{15}\left(100000\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(15)}+5\log_{15}\left(10\right)$$

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