Datrys 15^t=16

$$15 ^ { t } = 16$$

Datrys ar gyfer t

$$t=4\log_{15}\left(2\right)\approx 1.023832099$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$15^{t}=16$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(15^{t})=\log(16)$$

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

$$t\log(15)=\log(16)$$

Rhannu’r ddwy ochr â \log(15).

$$t=\frac{\log(16)}{\log(15)}$$

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

$$t=\log_{15}\left(16\right)$$

Datrys ar gyfer t (complex solution)

$$t=\frac{2\pi n_{1}i}{\ln(15)}+4\log_{15}\left(2\right)$$

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