Datrys frac{5^{m}*5^3*5^-2}{5^-5}=5^12

$$\frac { 5 ^ { m } \times 5 ^ { 3 } \times 5 ^ { - 2 } } { 5 ^ { - 5 } } = 5 ^ { 12 }$$

Datrys ar gyfer m

$$m=6$$

Camau gan Ddefnyddio Diffiniad Logarithm

Er mwyn lluosi pwerau sy’n rhannu’r un sail, adiwch eu esbonyddion. Adiwch 3 a -2 i gael 1.

$$\frac{5^{m}\times 5^{1}}{5^{-5}}=5^{12}$$

Er mwyn rhannu pwerau sy’n rhannu’r un sail, tynnwch esbonydd yr enwadur o esbonydd y rhifiadur.

$$5^{6}\times 5^{m}=5^{12}$$

Cyfrifo 5 i bŵer 12 a chael 244140625.

$$5^{6}\times 5^{m}=244140625$$

Cyfrifo 5 i bŵer 6 a chael 15625.

$$15625\times 5^{m}=244140625$$

Rhannu’r ddwy ochr â 15625.

$$5^{m}=\frac{244140625}{15625}$$

Rhannu 244140625 â 15625 i gael 15625.

$$5^{m}=15625$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{m})=\log(15625)$$

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

$$m\log(5)=\log(15625)$$

Rhannu’r ddwy ochr â \log(5).

$$m=\frac{\log(15625)}{\log(5)}$$

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

$$m=\log_{5}\left(15625\right)$$