Datrys 0.99+left(1-0.25right)^N=1

$$0.99+{\left(1-0.25\right)}^{N}=1$$

Datrys ar gyfer N

$$N=-2\log_{0.75}\left(10\right)\approx 16.007845559$$

Camau gan Ddefnyddio Diffiniad Logarithm

Tynnu 0.25 o 1 i gael 0.75.

$$0.99+0.75^{N}=1$$

Tynnu 1 o'r ddwy ochr.

$$0.99+0.75^{N}-1=0$$

Tynnu 1 o 0.99 i gael -0.01.

$$-0.01+0.75^{N}=0$$

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$0.75^{N}-0.01=0$$

Adio 0.01 at ddwy ochr yr hafaliad.

$$0.75^{N}=0.01$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(0.75^{N})=\log(0.01)$$

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

$$N\log(0.75)=\log(0.01)$$

Rhannu’r ddwy ochr â \log(0.75).

$$N=\frac{\log(0.01)}{\log(0.75)}$$

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

$$N=\log_{0.75}\left(0.01\right)$$